Sometime ago Jonathan Oppenheim, one of the brightest minds [1, 2, 3, 4, 5, 6, 7, 8, 9] in the frontiers of quantum information and quantum foundations, posted a very interesting article [10] on arXiv. As is the custom these days, he announced the paper in a series of tweets, starting with:

A post-quantum theory of classical gravity? https://t.co/uNbsbZ2AYq

A consistent theory of classical gravity coupled to quantum field theory that reduces to Einstein’s equations in the classical limit. The assumption that gravity is classical necessarily modifies quantum 1/3

— Jonathan Oppenheim (@postquantum) November 9, 2018

Now, while the work itself is a tour de force of mathematical and physical insight, in my humble opinion, there are several shortcomings in the basic idea. I mentioned these shortcomings in brief in my own series of tweets:

There are several problems with this idea. I will list them here and elaborate on them elsewhere. https://t.co/7Emx08julE

— Astroboy (@lqgist) November 10, 2018

This post is about elaborating on these points as I promised in my tweet.

There are two major parts of Oppenheim’s work which are subject to criticism. The first is the assumption that:

“since space-time describes causal structure and relationships between the matter degrees of freedom, that it is a-priori and fundamentally classical.”

If, for the sake of argument, one grants the possibility that space-time is a-priori and fundamentally classical, then the next question is to ask whether Oppenheim’s proposed framework for quantum matter coupled to stochastic classical gravity can avoid the pitfalls faced by classical gravity. In this post I will address the first aspect – must gravity be quantum?

# Must Gravity Be Quantum?

This, of course, is the crux of the matter. *Must*, after all, gravity be quantum or *must* it be quantized? There are the classic papers on this such as the argument for the necessity for quantum gravity by Hannah and Eppley [11] which unfortunately was shown to be flawed ^{1} by Mattingly [12]. There are several other very good motivations for seeking a quantum theory of gravity. Let us look at some of these.

## Singular Spacetimes

The best indicator of the range of validity of any physical theory is the point when the equations of that theory fail to provide physically reasonable solutions. For classical electromagnetism, this point occurs when one tries to describe the phenomenon of black body radiation in terms of equipartition of energy between the different radiation modes in a black body cavity. The resulting expression for the black body spectrum, called the Rayleigh-Jeans law, gives the right answer for the total emissivity of the black body at low wavelengths, but fails completely as we go to lower wavelengths and thus higher frequencies. The resolution of this difficulty lay in Planck’s quantum hypothesis and his resulting modification of the Rayleigh-Jeans distribution.

Another failure of classical physics is in the planetary model of atomic structure. If electrons are to be thought of as orbiting a positively charged nucleus, then – since any any accelerating charged particle emits radiation, and a particle in a circular orbit is undergoing constant acceleration – should they not continuously emit radiation causing their orbits to collapse into the nucleus? Clearly, this does not happen because we observe the existence of stable states of matter around us rather than short-lived states which collapse and die in massive bursts of energy.

Classical gravity experiences analogous failures in regions of spacetime where energy densities and temperatures are very high. Such regions correspond either to the interiors of black holes or the big bang/crunch at the start/end of the Universe. Both, black holes and cosmological spacetimes, generically possess *singularities* – regions of spacetime where the background curvature increases without bound. The hope is that a theory of quantum gravity would permit a modification of the notion of a smooth and continuous geometry in such a way that regions where singularities *would* have formed in the classical description would instead be described in terms of a quantum gravitational state where the spacetime does not possess a unique metric but is instead described by a superposition of fluctuating metrics.

While the classical geometry in such a region would be ill-defined, physical evolution of states of matter and geometry in such a region would certainly be well-defined.

## Hawking Radiation and Black Hole Evaporation

Classical gravity cannot account for the non-zero entropy of black holes. A non-zero entropy of any system implies the existence of microstates. While the horizon of Schwarzschild black hole solution of Einstein’s equation is a smooth surface, the non-zero entropy of the black hole [13, 14] implies that the apparently smooth surface must instead consist of many small pieces, each an independent degree of freedom which can contribute to the overall heat content and, thereby, to the total entropy of the system. The non-zero entropy arises from the fact that these small pieces can be arranged in many different way to yield the same macroscopic horizon structure.

Soon after Bekenstein’s discovery of the existence of black hole entropy, Hawking realized [15, 16] that the horizon would not be stable with respect to fluctuations of quantum fields in its vicinity. Particle-antiparticle pairs created from fluctuations of the vacuum quantum fields close to the horizon, would not annihilate as would be the case in flat space. Instead, one member of the pair would be pulled into the horizon, while the other would escape to infinity. It turns out that, with respect to an observer at infinity, the particle falling into the black hole has a *negative energy* (because inside the horizon time-like directions become space-like and vice-versa). Such an asymptotic observer would see a flux of particles coming out of the black hole whose mass (and area) would simultaneously be shrinking.

However, analogously to what happens in the problem of classical black body radiation, the endpoint of the Hawking evaporation process cannot be described consistently within the framework of quantum fields on curved space which works so well to predict the existence of Hawking radiation in the first place. The temperature of the black hole is inversely proportional to its mass. Thus as its mass reduces, the temperature increases without bound and the black hole must emit an infinite amount of energy before it completely evaporates.

This is reminiscent of the “ultraviolet” catastrophe of the late 19^{th} century. Once again, the hope is that quantum gravity would regularize the process of late-term evaporation of a black hole in much the same way that Planck’s introduction of the quantum hypothesis, and the resulting replacement of the Maxwell-Boltzmann distribution by the Bose-Einstein distribution for bosons, regulated the high-frequency behavior of the radiation flux of a black body. In the case of the black body problem the “ultraviolet catastrophe” is prevented by dropping the assumption that black body radiation can be emitted as electromagnetic waves of *any* frequency. Similarly, here the “Hawking radiation catastrophe” can be resolved by dropping the unstated assumption that geometric observables such as areas and volumes can take values in a continuum, and instead are *quantized* taking on only certain discrete values.

## Holography and AdS/CFT

There is by now a vast amount of evidence for the so-called “AdS/CFT” or “holographic” or Maldacena conjecture, according to which the physics of a bulk spacetime can be encoded into a field theory living on the boundary surface of that spacetime. The roots of this conjecture can be traced back to the problem of black hole entropy and questions raised by the existence of Bekenstein’s relation. The fact that the entropy of a black hole depends on the *area* of its boundary (the “horizon”), rather than on the *volume* contained within the boundary – as is the case with ordinary thermodynamic systems such as an ideal gas – already points us in the direction of a “holographic” viewpoint of black hole physics.

Reasoning along these lines propelled first Gerard ‘t Hooft in 1993 [17] and shortly thereafter Leonard Susskind in 1994 [18] to formulate what is now referred to as the “holographic conjecture”. A few years later Maldacena provided the first explicit example [19] of how holography could be used to calculate expectation values of physical observables (“Wilson loops” in his original paper) living in the boundary field theory of a five-dimensional bulk spacetime with Anti-de Sitter (AdS) geometry. Shortly thereafter work by Gubser, Klebanov, Polyakov and Witten [20, 21] provided the first general recipe for how correlation functions in boundary field theories could be calculated by understanding the behavior of gravitational fields in the bulk.

As of now, the holographic conjecture is no longer considered a “conjecture”, given the *vast* amount of evidence [22, 23, 24, 25] that has accumulated in its favor over the past two decades. In fact, we are at a stage where serious proposals [26, 27] have been put forward for how to observe AdS/CFT in the laboratory!

What is relevant for our discussion is that the holographic conjecture necessarily *implies* that any gravitational system possesses only a finite number of degrees of freedom. This is only possible if:

- There exists a minimal length scale at beyond which one cannot continue zooming into the spacetime manifold. Geometric observables such as lengths, areas and volumes are necessarily quantized at this scale.
- A quantum theory of gravity cannot be given a description in terms of a field theory which has a infinite number of degrees of freedom in any given region.

Given the overwhelming preponderance of evidence coming from the three lines of argument presented above – singularity resolution, Hawking radiation and holography – that spacetime is discrete at the smallest scales it would appear to be unwise to attempt to construct a theory of quantum gravity in which the gravitational field is inherently classical and smooth. Nevertheless, Oppenheim has taken on this daunting challenge and his proposal does provide food for thought and forces us to re-examine our conclusion that gravity must be quantized and the steps leading up to this conclusion. In order to understand his proposal better we need to understand the basic idea behind the theory of “semi-classical” gravity. That, however, will the topic of another blog post 🙂

[Bibtex]

```
@article{Horodecki2005Quantum,
Abstract = {Given an unknown quantum state distributed over two
systems, we determine how much quantum communication is
needed to transfer the full state to one system. This
communication measures the "partial information" one system
needs conditioned on it's prior information. It turns out
to be given by an extremely simple formula, the conditional
entropy. In the classical case, partial information must
always be positive, but we find that in the quantum world
this physical quantity can be negative. If the partial
information is positive, its sender needs to communicate
this number of quantum bits to the receiver; if it is
negative, the sender and receiver instead gain the
corresponding potential for future quantum communication.
We introduce a primitive "quantum state merging" which
optimally transfers partial information. We show how it
enables a systematic understanding of quantum network
theory, and discuss several important applications
including distributed compression, multiple access channels
and multipartite assisted entanglement distillation
(localizable entanglement). Negative channel capacities
also receive a natural interpretation.},
Archiveprefix = {arXiv},
Author = {Horodecki, Michal and Oppenheim, Jonathan and Winter, Andreas},
Citeulike-Article-Id = {277446},
Citeulike-Linkout-0 = {http://arxiv.org/abs/quant-ph/0505062},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/quant-ph/0505062},
Date-Added = {2012-04-16 17:37:59 +0530},
Date-Modified = {2012-04-16 17:38:00 +0530},
Day = {9},
Eprint = {quant-ph/0505062},
Keywords = {conditional\_entropy, information\_theory, partial\_information, quantum\_information, state\_merging},
Month = may,
Posted-At = {2011-10-21 04:18:30},
Priority = {2},
Title = {Quantum information can be negative},
Url = {http://arxiv.org/abs/quant-ph/0505062},
Year = {2005},
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```

[Bibtex]

```
@article{Oppenheim2010For-quantum,
Abstract = {Superactivation is the phenomenon where two quantum
channels which individually have zero-capacity can have
positive capacity when used together. The perspective given
here provides an intuitive explanation of this discovery by
Smith and Yard, and gives a protocol to activate any
private channel.},
Archiveprefix = {arXiv},
Author = {Oppenheim, Jonathan},
Citeulike-Article-Id = {3343539},
Citeulike-Linkout-0 = {http://arxiv.org/abs/1004.0052},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/1004.0052},
Citeulike-Linkout-2 = {http://dx.doi.org/10.1126/science.1164543},
Citeulike-Linkout-3 = {http://www.sciencemag.org/cgi/content/abstract/321/5897/1783},
Date-Added = {2010-04-11 11:11:21 +0530},
Date-Modified = {2018-12-23 01:42:18 +0530},
Day = {1},
Doi = {10.1126/science.1164543},
Eprint = {1004.0052},
Journal = {Science},
Keywords = {channel\_capacity, protocol, quantum\_information, superactivation, zero-capacity},
Local-Url = {/Users/deepak/ownCloud/root/research/bibdesk/Oppenheim.J_For quantum information, two wrongs can make a right_2010a.pdf},
Month = {Apr},
Number = {5897},
Pages = {1783--1784},
Posted-At = {2010-04-11 06:40:45},
Priority = {2},
Title = {For quantum information, two wrongs can make a right},
Url = {http://dx.doi.org/10.1126/science.1164543},
Volume = {321},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1126/science.1164543}}
```

[Bibtex]

```
@article{Oppenheim2010The-uncertainty,
Abstract = {Two central concepts of quantum mechanics are Heisenberg's
uncertainty principle, and a subtle form of non-locality
that Einstein famously called ``spooky action at a
distance''. These two fundamental features have thus far
been distinct concepts. Here we show that they are
inextricably and quantitatively linked. Quantum mechanics
cannot be more non-local with measurements that respect the
uncertainty principle. In fact, the link between
uncertainty and non-locality holds for all physical
{theories.More} specifically, the degree of non-locality of
any theory is determined by two factors -- the strength of
the uncertainty principle, and the strength of a property
called ``steering'', which determines which states can be
prepared at one location given a measurement at another.},
Archiveprefix = {arXiv},
Author = {Oppenheim, Jonathan and Wehner, Stephanie},
Citeulike-Article-Id = {8273657},
Citeulike-Linkout-0 = {http://arxiv.org/abs/1004.2507},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/1004.2507},
Citeulike-Linkout-2 = {http://dx.doi.org/10.1126/science.1192065},
Citeulike-Linkout-3 = {http://www.sciencemag.org/content/330/6007/1072.abstract},
Citeulike-Linkout-4 = {http://www.sciencemag.org/content/330/6007/1072.full.pdf},
Citeulike-Linkout-5 = {http://view.ncbi.nlm.nih.gov/pubmed/21097930},
Citeulike-Linkout-6 = {http://www.hubmed.org/display.cgi?uids=21097930},
Date-Added = {2016-09-08 07:14:28 +0000},
Date-Modified = {2016-09-08 12:44:29 +0530},
Day = {19},
Doi = {10.1126/science.1192065},
Eprint = {1004.2507},
Issn = {0036-8075},
Journal = {Science},
Keywords = {entanglement, heisenberg, nonlocality, oppenheim\_jonathan, quantum\_foundations, quantum\_games, quantum\_mechanics, quantum\_steering, uncertainty\_principle, wehner\_stephanie},
Month = nov,
Number = {6007},
Pages = {1072--1074},
Pmid = {21097930},
Posted-At = {2016-09-08 08:14:21},
Priority = {2},
Publisher = {American Association for the Advancement of Science},
Title = {The uncertainty principle determines the non-locality of quantum mechanics},
Url = {http://dx.doi.org/10.1126/science.1192065},
Volume = {330},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1126/science.1192065}}
```

[Bibtex]

```
@article{Horodecki2011Fundamental,
Abstract = {The relationship between thermodynamics and statistical
physics is valid in the thermodynamic limit - when the
number of particles becomes very large. Here, we study
thermodynamics in the opposite regime - at both the nano
scale, and when quantum effects become important. Applying
results from quantum information theory we construct a
theory of thermodynamics in these limits. We derive general
criteria for thermodynamical state transformations, and as
special cases, find two free energies: one that quantifies
the deterministically extractable work from a small system
in contact with a heat bath, and the other that quantifies
the reverse process. We find that there are fundamental
limitations on work extraction from nonequilibrium states,
owing to finite size effects and quantum coherences. This
implies that thermodynamical transitions are generically
irreversible at this scale. As one application of these
methods, we analyse the efficiency of small heat engines
and find that they are irreversible during the adiabatic
stages of the cycle.},
Author = {Horodecki, Micha{\l} and Oppenheim, Jonathan},
Date-Added = {2014-12-13 19:04:25 +0000},
Date-Modified = {2014-12-14 00:34:35 +0530},
Doi = {10.1038/ncomms3059},
File = {FULLTEXT:/home/dvaid/almostaphysicist.com/i-librarian/library/02108.pdf:PDF},
Journal = {Nature Communications 4, 2059 (2013)},
Title = {Fundamental limitations for quantum and nano thermodynamics},
Year = {2011},
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Bdsk-Url-1 = {http://dx.doi.org/10.1038/ncomms3059}}
```

[Bibtex]

```
@article{Brandao2013The-second,
Abstract = {The second law of thermodynamics tells us which state
transformations are so statistically unlikely that they are
effectively forbidden. Its original formulation, due to
Clausius, states that "Heat can never pass from a colder to
a warmer body without some other change, connected
therewith, occurring at the same time". The second law
applies to systems composed of many particles interacting;
however, we are seeing that one can make sense of
thermodynamics in the regime where we only have a small
number of particles interacting with a heat bath. Is there
a second law of thermodynamics in this regime? Here, we
find that for processes which are cyclic or very close to
cyclic, the second law for microscopic systems takes on a
very different form than it does at the macroscopic scale,
imposing not just one constraint on what state
transformations are possible, but an entire family of
constraints. In particular, we find a family of free
energies which generalise the traditional one, and show
that they can never increase. We further find that there
are three regimes which determine which family of second
laws govern state transitions, depending on how cyclic the
process is. In one regime one can cause an apparent
violation of the usual second law, through a process of
embezzling work from a large system which remains
arbitrarily close to its original state. These second laws
are not only relevant for small systems, but also apply to
individual macroscopic systems interacting via long-range
interactions, which only satisfy the ordinary second law on
average. By making precise the definition of thermal
operations, the laws of thermodynamics take on a simple
form with the first law defining the class of thermal
operations, the zeroeth law emerging as a unique condition
ensuring the theory is nontrivial, and the remaining laws
being a monotonicity property of our generalised free
energies.},
Archiveprefix = {arXiv},
Arxivid = {1305.5278},
Author = {Brandao, Fernando G. S. L. and Horodecki, Micha{\l} and Ng, Nelly Huei Ying and Oppenheim, Jonathan and Wehner, Stephanie},
Date-Added = {2018-01-10 06:13:41 +0000},
Date-Modified = {2018-01-10 06:13:52 +0000},
Doi = {10.1073/pnas.1411728112},
Eprint = {1305.5278},
File = {:Users/deepak/mendeley/files/Brandao et al.{\_}The second laws of quantum thermodynamics{\_}2013.pdf:pdf},
Isbn = {9781137332875},
Issn = {0027-8424},
Journal = {Proceedings of the National Academy of Sciences},
Mendeley-Groups = {Quantum Thermodynamics},
Number = {11},
Pages = {3275--3279},
Pmid = {25675476},
Title = {{The second laws of quantum thermodynamics}},
Url = {http://m.pnas.org/content/112/11/3275.abstract http://www.pnas.org/lookup/doi/10.1073/pnas.1411728112 http://arxiv.org/abs/1305.5278{\%}0Ahttp://dx.doi.org/10.1073/pnas.1411728112},
Volume = {112},
Year = {2013},
Bdsk-Url-1 = {https://dx.doi.org/10.1073/pnas.1411728112}}
```

[Bibtex]

```
@article{Kollmeier2014Photon,
Abstract = {We examine the statistics of the low-redshift Lyman-alpha
forest from smoothed particle hydrodynamic simulations in
light of recent improvements in the estimated evolution of
the cosmic ultraviolet background (UVB) and recent
observations from the Cosmic Origins Spectrograph (COS). We
find that the value of the metagalactic photoionization
rate required by our simulations to match the observed
properties of the low-redshift Lyman-alpha forest is a
factor of 5 larger than the value predicted by state-of-the
art models for the evolution of this quantity. This
mismatch results in the mean flux decrement of the
Lyman-alpha forest being underpredicted by at least a
factor of 2 (a 10-sigma discrepancy with observations) and
a column density distribution of Lyman-alpha forest
absorbers systematically and significantly elevated
compared to observations over nearly two decades in column
density. We examine potential resolutions to this mismatch
and find that either conventional sources of ionizing
photons (galaxies and quasars) must be significantly
elevated relative to current observational estimates or our
theoretical understanding of the low-redshift universe is
in need of substantial revision.},
Author = {Kollmeier, Juna A. and Weinberg, David H. and Oppenheimer, Benjamin D. and Haardt, Francesco and Katz, Neal and Dav{\'e}, Romeel A. and Fardal, Mark and Madau, Piero and Danforth, Charles and Ford, Amanda B. and Peeples, Molly S. and McEwen, Joseph},
File = {FULLTEXT:/home/dvaid/almostaphysicist.com/librarian3.0/library/01864.pdf:PDF},
Owner = {deepak},
Timestamp = {2014.08.14},
Title = {The Photon Underproduction Crisis},
Year = {2014}}
```

[Bibtex]

```
@article{Yunger-Halpern2016Microcanonical,
Abstract = {The grand canonical ensemble lies at the core of quantum
and classical statistical mechanics. A small system
thermalizes to this ensemble while exchanging heat and
particles with a bath. A quantum system may exchange
quantities represented by operators that fail to commute.
Whether such a system thermalizes and what form the thermal
state has are questions about truly quantum thermodynamics.
Here we investigate this thermal state from three
perspectives. First, we introduce an approximate
microcanonical ensemble. If this ensemble characterizes the
system-and-bath composite, tracing out the bath yields the
system's thermal state. This state is expected to be the
equilibrium point, we argue, of typical dynamics. Finally,
we define a resource-theory model for thermodynamic
exchanges of noncommuting observables. Complete
passivity---the inability to extract work from equilibrium
states---implies the thermal state's form, too. Our work
opens new avenues into equilibrium in the presence of
quantum noncommutation.},
Archiveprefix = {arXiv},
Arxivid = {1512.01189},
Author = {{Yunger Halpern}, Nicole and Faist, Philippe and Oppenheim, Jonathan and Winter, Andreas},
Date-Added = {2018-01-10 06:13:41 +0000},
Date-Modified = {2018-01-10 06:13:52 +0000},
Doi = {10.1038/ncomms12051},
Eprint = {1512.01189},
File = {:Users/deepak/mendeley/files/Yunger Halpern et al.{\_}Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charg.pdf:pdf},
Isbn = {9781137332875},
Issn = {20411723},
Journal = {Nature Communications},
Mendeley-Groups = {Quantum Thermodynamics},
Pmid = {27384494},
Title = {{Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges}},
Url = {http://arxiv.org/abs/1512.01189 http://dx.doi.org/10.1038/ncomms12051 https://arxiv.org/abs/1512.01189},
Volume = {7},
Year = {2016},
Bdsk-Url-1 = {http://arxiv.org/abs/1512.01189%20http://dx.doi.org/10.1038/ncomms12051%20https://arxiv.org/abs/1512.01189},
Bdsk-Url-2 = {https://dx.doi.org/10.1038/ncomms12051}}
```

[Bibtex]

```
@article{Woods2016Autonomous,
Abstract = {Processes such as quantum computation, or the evolution of
quantum cellular automata are typically described by a
unitary operation implemented by an external observer. In
particular, an interaction is generally turned on for a
precise amount of time, using a classical clock. A fully
quantum mechanical description of such a device would
include a quantum description of the clock whose state is
generally disturbed because of the back-reaction on it.
Such a description is needed if we wish to consider finite
sized autonomous quantum machines requiring no external
control. The extent of the back-reaction has implications
on how small the device can be, on the length of time the
device can run, and is required if we want to understand
what a fully quantum mechanical treatment of an observer
would look like. Here, we consider the implementation of a
unitary by a finite sized device, and show that the
back-reaction on it can be made exponentially small in the
device's dimension with only a linear increase in energy.
As a result, an autonomous quantum machine need only be of
modest size and or energy. We are also able to solve a
long-standing open problem by using a finite sized quantum
clock to approximate the continuous evolution of an
idealised clock. The result has implications on the
equivalence of different paradigms of quantum
thermodynamics, some which allow external control and some
which only allow autonomous thermal machines.},
Archiveprefix = {arXiv},
Arxivid = {1607.04591},
Author = {Woods, Mischa P. and Silva, Ralph and Oppenheim, Jonathan},
Date-Added = {2018-03-28 04:58:29 +0000},
Date-Modified = {2018-03-28 04:58:32 +0000},
Eprint = {1607.04591},
File = {:Users/deepak/mendeley/Woods, Silva, Oppenheim{\_}Autonomous quantum machines and finite sized clocks{\_}2016.pdf:pdf},
Mendeley-Groups = {Computational Universe},
Month = {jul},
Title = {{Autonomous quantum machines and finite sized clocks}},
Url = {http://arxiv.org/abs/1607.04591},
Year = {2016},
Bdsk-Url-1 = {http://arxiv.org/abs/1607.04591}}
```

[Bibtex]

```
@article{Masanes2017A-general,
Abstract = {The third law of thermodynamics has a controversial past
and a number of formulations due to Planck, Einstein, and
Nernst. It's most accepted version, the unattainability
principle, states that "any thermodynamic process cannot
reach the temperature of absolute zero by a finite number
of steps and within a finite time." Although formulated in
1912, there has been no general proof of the principle, and
the only evidence we have for it is that particular cooling
methods become less efficient as the temperature decreases.
Here we provide the first derivation of a general
unattainability principle, which applies to arbitrary
cooling processes, even those exploiting the laws of
quantum mechanics or involving an infinite-dimensional
reservoir. We quantify the resources needed to cool a
system to any particular temperature, and translate these
resources into a minimal time or number of steps by
considering the notion of a Thermal Machine which obeys
similar restrictions to universal computers. We generally
find that the obtainable temperature can scale as an
inverse power of the cooling time. Our argument relies on
the heat capacity of the bath being positive, and we show
that if this is not the case then perfect cooling in finite
time is in principle possible. Our results also clarify the
connection between two versions of the third law (the
Unattainability Principle and the Heat Theorem), and place
ultimate bounds on the speed at which information can be
erased.},
Archiveprefix = {arXiv},
Arxivid = {1412.3828},
Author = {Masanes, Llu{\'{i}}s and Oppenheim, Jonathan},
Date-Added = {2018-01-10 06:13:41 +0000},
Date-Modified = {2018-01-10 06:13:52 +0000},
Doi = {10.1038/ncomms14538},
Eprint = {1412.3828},
File = {:Users/deepak/mendeley/files/Masanes, Oppenheim{\_}A general derivation and quantification of the third law of thermodynamics{\_}2017.pdf:pdf},
Issn = {20411723},
Journal = {Nature Communications},
Mendeley-Groups = {Quantum Thermodynamics},
Pages = {14538},
Pmid = {28290452},
Title = {{A general derivation and quantification of the third law of thermodynamics}},
Url = {http://www.nature.com/doifinder/10.1038/ncomms14538 https://www.nature.com/articles/ncomms14538},
Volume = {8},
Year = {2017},
Bdsk-Url-1 = {http://www.nature.com/doifinder/10.1038/ncomms14538%20https://www.nature.com/articles/ncomms14538},
Bdsk-Url-2 = {https://dx.doi.org/10.1038/ncomms14538}}
```

[Bibtex]

```
@article{Oppenheim2018A-post-quantum,
Abstract = {We present a consistent theory of classical gravity
coupled to quantum field theory. The dynamics is linear in
the density matrix, completely positive and
trace-preserving, and reduces to Einstein's equations in
the classical limit. The constraints of general relativity
are imposed as a symmetry on the equations of motion. The
assumption that gravity is classical necessarily modifies
the dynamical laws of quantum mechanics -- the theory must
be fundamentally stochastic involving finite sized and
probabilistic jumps in space-time and in the quantum field.
Nonetheless the quantum state of the system can remain pure
conditioned on the classical degrees of freedom. The
measurement postulate of quantum mechanics is not needed
since the interaction of the quantum degrees of freedom
with classical space-time necessarily causes collapse of
the wave-function. More generally, we derive a form of
classical-quantum dynamics using a non-commuting divergence
which has as its limit deterministic classical Hamiltonian
evolution, and which doesn't suffer from the pathologies of
the semi-classical theory.},
Archiveprefix = {arXiv},
Arxivid = {1811.03116},
Author = {Oppenheim, Jonathan},
Date-Added = {2018-11-14 19:04:48 +0530},
Date-Modified = {2018-11-14 19:04:50 +0530},
Eprint = {1811.03116},
File = {:Users/deepak/mendeley/Oppenheim{\_}A post-quantum theory of classical gravity{\_}2018.pdf:pdf},
Month = {nov},
Title = {{A post-quantum theory of classical gravity?}},
Url = {http://arxiv.org/abs/1811.03116 https://www.arxiv-vanity.com/papers/1811.03116/},
Year = {2018},
Bdsk-Url-1 = {http://arxiv.org/abs/1811.03116%20https://www.arxiv-vanity.com/papers/1811.03116/}}
```

[Bibtex]

```
@article{Eppley1977The-necessity,
Abstract = {The assumption that a classical gravitational field
interacts with a quantum system is shown to lead to
violations of either momentum conservation or the
uncertainty principle, or to result in transmission of
signals faster thanc. A similar argument holds for the
electromagnetic field.},
Author = {Eppley, Kenneth and Hannah, Eric},
Date-Added = {2018-11-15 00:07:13 +0530},
Date-Modified = {2018-11-15 00:07:14 +0530},
Doi = {10.1007/BF00715241},
File = {:Users/deepak/mendeley/Eppley, Hannah{\_}The necessity of quantizing the gravitational field{\_}1977.pdf:pdf},
Issn = {00159018},
Journal = {Foundations of Physics},
Month = {feb},
Number = {1-2},
Pages = {51--68},
Publisher = {Kluwer Academic Publishers-Plenum Publishers},
Title = {{The necessity of quantizing the gravitational field}},
Url = {http://link.springer.com/10.1007/BF00715241},
Volume = {7},
Year = {1977},
Bdsk-Url-1 = {http://link.springer.com/10.1007/BF00715241},
Bdsk-Url-2 = {https://doi.org/10.1007/BF00715241}}
```

[Bibtex]

```
@article{Mattingly2006Why-Eppley,
Abstract = {It is shown that Eppley and Hannah's thought experiment
establishing that gravity must be quantized is fatally
flawed. The device they propose, even if built, cannot
establish their claims, nor is it plausible that it can be
built with any materials compatible with the values of c,
h, and G. Finally the device, and any reasonable
modification of it, would be so massive as to be within its
own Schwarzschild radius-a fatal flaw for any thought
experiment.},
Archiveprefix = {arXiv},
Arxivid = {gr-qc/0601127},
Author = {Mattingly, James},
Date-Added = {2018-11-15 00:07:13 +0530},
Date-Modified = {2018-11-15 00:07:14 +0530},
Doi = {10.1103/PhysRevD.73.064025},
Eprint = {0601127},
File = {:Users/deepak/mendeley/Mattingly{\_}Why Eppley and Hannah's thought experiment fails{\_}2006.pdf:pdf},
Issn = {15507998},
Journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
Month = {jan},
Number = {6},
Primaryclass = {gr-qc},
Title = {{Why Eppley and Hannah's thought experiment fails}},
Url = {http://arxiv.org/abs/gr-qc/0601127 http://dx.doi.org/10.1103/PhysRevD.73.064025},
Volume = {73},
Year = {2006},
Bdsk-Url-1 = {http://arxiv.org/abs/gr-qc/0601127%20http://dx.doi.org/10.1103/PhysRevD.73.064025},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevD.73.064025}}
```

[Bibtex]

```
@article{Bekenstein1972Black,
Author = {Bekenstein, J.},
Citeulike-Article-Id = {9648076},
Citeulike-Linkout-0 = {http://dx.doi.org/10.1007/BF02757029},
Citeulike-Linkout-1 = {http://www.springerlink.com/content/72373140225885h3},
Date-Added = {2011-08-12 15:03:51 +0930},
Date-Modified = {2011-08-12 11:03:52 +0530},
Day = {1},
Doi = {10.1007/BF02757029},
Issn = {0375-930X},
Journal = {Lettere Al Nuovo Cimento (1971 -- 1985)},
Keywords = {bekenstein, black\_hole\_entropy, black\_holes, classic, second\_law},
Month = aug,
Number = {15},
Pages = {737--740},
Posted-At = {2011-08-12 06:33:32},
Priority = {2},
Publisher = {Italian Physical Society},
Title = {Black holes and the second law},
Url = {http://dx.doi.org/10.1007/BF02757029},
Volume = {4},
Year = {1972},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF02757029}}
```

[Bibtex]

```
@article{Bekenstein1973Black,
Abstract = {There are a number of similarities between black-hole
physics and thermodynamics. Most striking is the similarity
in the behaviors of black-hole area and of entropy: Both
quantities tend to increase irreversibly. In this paper we
make this similarity the basis of a thermodynamic approach
to black-hole physics. After a brief review of the elements
of the theory of information, we discuss black-hole physics
from the point of view of information theory. We show that
it is natural to introduce the concept of black-hole
entropy as the measure of information about a black-hole
interior which is inaccessible to an exterior observer.
Considerations of simplicity and consistency, and
dimensional arguments indicate that the black-hole entropy
is equal to the ratio of the black-hole area to the square
of the Planck length times a dimensionless constant of
order unity. A different approach making use of the
specific properties of Kerr black holes and of concepts
from information theory leads to the same conclusion, and
suggests a definite value for the constant. The physical
content of the concept of black-hole entropy derives from
the following generalized version of the second law: When
common entropy goes down a black hole, the common entropy
in the black-hole exterior plus the black-hole entropy
never decreases. The validity of this version of the second
law is supported by an argument from information theory as
well as by several examples.},
Author = {Bekenstein, Jacob D.},
Citeulike-Article-Id = {4131591},
Citeulike-Linkout-0 = {http://dx.doi.org/10.1103/PhysRevD.7.2333},
Citeulike-Linkout-1 = {http://link.aps.org/abstract/PRD/v7/i8/p2333},
Citeulike-Linkout-2 = {http://link.aps.org/pdf/PRD/v7/i8/p2333},
Date-Added = {2011-08-12 15:02:27 +0930},
Date-Modified = {2011-08-12 11:02:28 +0530},
Day = {15},
Doi = {10.1103/PhysRevD.7.2333},
Journal = {Physical Review D},
Keywords = {area\_law, bekenstein, black\_hole\_entropy, classic, information\_theory, thermodynamics},
Month = apr,
Number = {8},
Pages = {2333--2346},
Posted-At = {2011-08-12 06:32:13},
Priority = {2},
Publisher = {American Physical Society},
Title = {Black Holes and Entropy},
Url = {http://dx.doi.org/10.1103/PhysRevD.7.2333},
Volume = {7},
Year = {1973},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevD.7.2333}}
```

[Bibtex]

```
@article{Hawking1974Black,
Abstract = {QUANTUM gravitational effects are usually ignored in
calculations of the formation and evolution of black holes.
The justification for this is that the radius of curvature
of space-time outside the event horizon is very large
compared to the Planck length (Għ/c 3)1/2 ≈ 10−33 cm,
the length scale on which quantum fluctuations of the
metric are expected to be of order unity. This means that
the energy density of particles created by the
gravitational field is small compared to the space-time
curvature. Even though quantum effects may be small
locally, they may still, however, add up to produce a
significant effect over the lifetime of the Universe ≈
1017 s which is very long compared to the Planck time ≈
10−43 s. The purpose of this letter is to show that this
indeed may be the case: it seems that any black hole will
create and emit particles such as neutrinos or photons at
just the rate that one would expect if the black hole was a
body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6
(M/M)K where κ is the surface gravity of the black hole1.
As a black hole emits this thermal radiation one would
expect it to lose mass. This in turn would increase the
surface gravity and so increase the rate of emission. The
black hole would therefore have a finite life of the order
of 1071 (M/M)−3 s. For a black hole of solar mass this is
much longer than the age of the Universe. There might,
however, be much smaller black holes which were formed by
fluctuations in the early Universe2. Any such black hole of
mass less than 1015 g would have evaporated by now. Near
the end of its life the rate of emission would be very high
and about 1030 erg would be released in the last 0.1 s.
This is a fairly small explosion by astronomical standards
but it is equivalent to about 1 million 1 Mton hydrogen
bombs.},
Author = {Hawking, S. W.},
Date-Added = {2018-01-13 09:15:52 +0000},
Date-Modified = {2018-10-18 15:18:08 +0530},
Doi = {10.1038/248030a0},
File = {:Users/deepak/mendeley/files/Hawking{\_}Black hole explosions{\_}1974.pdf:pdf},
Issn = {0028-0836},
Journal = {Nature, Volume 248, Issue 5443, pp. 30-31 (1974).},
Number = {5443},
Pages = {30--31},
Title = {{Black hole explosions?}},
Url = {http://adsabs.harvard.edu/abs/1974Natur.248...30H). http://www.nature.com/doifinder/10.1038/248030a0},
Volume = {248},
Year = {1974},
Bdsk-Url-1 = {http://adsabs.harvard.edu/abs/1974Natur.248...30H).%20http://www.nature.com/doifinder/10.1038/248030a0},
Bdsk-Url-2 = {https://dx.doi.org/10.1038/248030a0}}
```

[Bibtex]

```
@article{Hawking1975Particle,
Abstract = {Abstract\ \ In the classical theory black holes
can only absorb and not emit particles. However it is shown
that quantum mechanical effects cause black holes to create
and emit particles as if they were hot bodies with
temperature \\$\\$\\frac{{h\\kappa }}{{2\\pi k}} \\approx
10^{ - 6} \\left( {\\frac{{M\_ {\o}dot }}{M}} \\right){}^
\\circ K\\$\\$ where {\^I}º is the surface gravity of the
black hole. This thermal emission leads to a slow decrease
in the mass of the black hole and to its eventual
disappearance: any primordial black hole of mass less than
about 1015 g would have evaporated by now. Although these
quantum effects violate the classical law that the area of
the event horizon of a black hole cannot decrease, there
remains a Generalized Second Law:S+1/4A never decreases
whereS is the entropy of matter outside black holes andA is
the sum of the surface areas of the event horizons. This
shows that gravitational collapse converts the baryons and
leptons in the collapsing body into entropy. It is tempting
to speculate that this might be the reason why the Universe
contains so much entropy per baryon.},
Author = {Hawking, S.},
Citeulike-Article-Id = {6444208},
Citeulike-Linkout-0 = {http://dx.doi.org/10.1007/BF02345020},
Day = {10},
Doi = {10.1007/BF02345020},
Journal = {Communications in Mathematical Physics},
Keywords = {bekenstein\_bound, black\_hole, entropy, event\_horizons, file-import-09-12-27, gravitational\_collapse, hawking\_radiation, quantum\_effects, quantum\_gravity, surface\_areas, thermal\_emission},
Month = {August},
Number = {3},
Pages = {199--220},
Posted-At = {2009-12-27 12:17:42},
Priority = {2},
Title = {Particle creation by black holes},
Url = {http://dx.doi.org/10.1007/BF02345020},
Volume = {43},
Year = {1975},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://dx.doi.org/10.1007/BF02345020}}
```

[Bibtex]

```
@article{t-Hooft1993Dimensional,
Abstract = {The requirement that physical phenomena associated with
gravitational collapse should be duly reconciled with the
postulates of quantum mechanics implies that at a Planckian
scale our world is not 3+1 dimensional. Rather, the
observable degrees of freedom can best be described as if
they were Boolean variables defined on a two-dimensional
lattice, evolving with time. This observation, deduced from
not much more than unitarity, entropy and counting
arguments, implies severe restrictions on possible models
of quantum gravity. Using cellular automata as an example
it is argued that this dimensional reduction implies more
constraints than the freedom we have in constructing
models. This is the main reason why so-far no completely
consistent mathematical models of quantum black holes have
been found. Essay dedicated to Abdus Salam.},
Archiveprefix = {arXiv},
Author = {'t Hooft, G.},
Citeulike-Article-Id = {521048},
Citeulike-Linkout-0 = {http://arxiv.org/abs/gr-qc/9310026},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/gr-qc/9310026},
Citeulike-Linkout-2 = {http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1993gr.qc....10026.},
Date-Added = {2010-05-26 20:43:36 +0530},
Date-Modified = {2018-12-23 01:47:29 +0530},
Day = {20},
Eprint = {gr-qc/9310026},
Keywords = {algebra, boolean, cellular\_automata, classic, dimensional\_reduction, holography, two\_dimensional},
Local-Url = {/Users/deepak/ownCloud/root/research/bibdesk/'t Hooft.G_Dimensional Reduction in Quantum Gravity_1993a.pdf},
Month = {Mar},
Posted-At = {2010-05-26 16:13:07},
Priority = {2},
Title = {Dimensional Reduction in Quantum Gravity},
Url = {http://arxiv.org/abs/gr-qc/9310026},
Year = {1993},
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Bdsk-Url-1 = {http://arxiv.org/abs/gr-qc/9310026}}
```

[Bibtex]

```
@article{Susskind1994The-World,
Abstract = {According to 't Hooft the combination of quantum mechanics
and gravity requires the three dimensional world to be an
image of data that can be stored on a two dimensional
projection much like a holographic image. The two
dimensional description only requires one discrete degree
of freedom per Planck area and yet it is rich enough to
describe all three dimensional phenomena. After outlining
't Hooft's proposal I give a preliminary informal
description of how it may be implemented. One finds a basic
requirement that particles must grow in size as their
momenta are increased far above the Planck scale. The
consequences for high energy particle collisions are
described. The phenomena of particle growth with momentum
was previously discussed in the context of string theory
and was related to information spreading near black hole
horizons. The considerations of this paper indicate that
the effect is much more rapid at all but the earliest
times. In fact the rate of spreading is found to saturate
the bound from causality. Finally we consider string theory
as a possible realization of 't Hooft's idea. The light
front lattice string model of Klebanov and Susskind is
reviewed and its similarities with the holographic theory
are demonstrated. The agreement between the two requires
unproven but plausible assumptions about the
nonperturbative behavior of string theory. Very similar
ideas to those in this paper have been long held by Charles
Thorn.},
Archiveprefix = {arXiv},
Author = {Susskind, L.},
Citeulike-Article-Id = {521046},
Citeulike-Linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal\&id=JMAPAQ000036000011006377000001\&idtype=cvips\&gifs=yes},
Citeulike-Linkout-1 = {http://link.aip.org/link/?JMP/36/6377},
Citeulike-Linkout-2 = {http://arxiv.org/abs/hep-th/9409089},
Citeulike-Linkout-3 = {http://arxiv.org/pdf/hep-th/9409089},
Citeulike-Linkout-4 = {http://dx.doi.org/10.1063/1.531249},
Date-Added = {2013-01-12 01:06:06 +0530},
Date-Modified = {2013-01-12 01:06:08 +0530},
Day = {28},
Doi = {10.1063/1.531249},
Eprint = {hep-th/9409089},
Issn = {00222488},
Journal = {Journal of Mathematical Physics},
Keywords = {bekenstein\_bound, black\_holes, classic, entropy, holography, quantum\_gravity, string\_theory, susskind, thooft},
Month = sep,
Number = {11},
Pages = {6377--6396},
Posted-At = {2013-01-11 19:34:55},
Priority = {2},
Publisher = {AIP},
Title = {The World as a Hologram},
Url = {http://dx.doi.org/10.1063/1.531249},
Volume = {36},
Year = {1994},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://dx.doi.org/10.1063/1.531249}}
```

[Bibtex]

```
@article{Maldacena1998Wilson,
Abstract = {We propose a method to calculate the expectation values of
an operator similar to the Wilson loop in the large N limit
of field theories. We consider N=4 3+1 dimensional
{super-Yang}-Mills. The prescription involves calculating
the area of a fundamental string worldsheet in certain
supergravity backgrounds. We also consider the case of
coincident M-theory fivebranes where one is lead to
calculating the area of M-theory two-branes. We briefly
discuss the computation for 2+1 dimensional
{super-Yang}-Mills with sixteen supercharges which is
non-conformal. In all these cases we calculate the energy
of quark-antiquark pair.},
Archiveprefix = {arXiv},
Author = {Maldacena, Juan M.},
Citeulike-Article-Id = {3038086},
Citeulike-Linkout-0 = {http://arxiv.org/abs/hep-th/9803002},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/hep-th/9803002},
Date-Added = {2011-03-12 15:42:43 +0530},
Date-Modified = {2011-03-12 15:42:44 +0530},
Day = {19},
Eprint = {hep-th/9803002},
Keywords = {adscft, expectation\_value, large\_n\_theories, string\_theory, supergravity, wilson\_loops, yang\_mills},
Month = mar,
Posted-At = {2011-03-12 10:12:12},
Priority = {2},
Title = {Wilson loops in large N field theories},
Url = {http://arxiv.org/abs/hep-th/9803002},
Year = {1998},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://arxiv.org/abs/hep-th/9803002}}
```

[Bibtex]

```
@article{Gubser1998Gauge,
Abstract = {We suggest a means of obtaining certain Green's functions
in 3+1-dimensional \${\cal N} = 4\$ supersymmetric
Yang-Mills theory with a large number of colors via
non-critical string theory. The non-critical string theory
is related to critical string theory in anti-deSitter
background. We introduce a boundary of the anti-deSitter
space analogous to a cut-off on the Liouville coordinate of
the two-dimensional string theory. Correlation functions of
operators in the gauge theory are related to the dependence
of the supergravity action on the boundary conditions. From
the quadratic terms in supergravity we read off the
anomalous dimensions. For operators that couple to massless
string states it has been established through absorption
calculations that the anomalous dimensions vanish, and we
rederive this result. The operators that couple to massive
string states at level \$n\$ acquire anomalous dimensions
that grow as \$2\left (n g\_{YM} \sqrt {2 N} )^{1/2}\$ for
large `t Hooft coupling. This is a new prediction about the
strong coupling behavior of large \$N\$ SYM theory.},
Archiveprefix = {arXiv},
Author = {Gubser, S. S. and Klebanov, I. R. and Polyakov, A. M.},
Citeulike-Article-Id = {514410},
Citeulike-Linkout-0 = {http://arxiv.org/abs/hep-th/9802109},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/hep-th/9802109},
Date-Added = {2011-03-03 12:52:53 +0530},
Date-Modified = {2011-03-03 12:52:54 +0530},
Day = {27},
Eprint = {hep-th/9802109},
Keywords = {adscft, classic, correlation\_functions, gauge\_theory, greens\_functions, holography, large\_n\_theories, string\_theory, strong\_coupling, susy, yang\_mills},
Month = mar,
Posted-At = {2011-03-03 07:21:13},
Priority = {2},
Title = {Gauge Theory Correlators from {Non-Critical} String Theory},
Url = {http://arxiv.org/abs/hep-th/9802109},
Year = {1998},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://arxiv.org/abs/hep-th/9802109}}
```

[Bibtex]

```
@article{Witten1998Anti,
Abstract = {Recently, it has been proposed by Maldacena that large
\$N\$ limits of certain conformal field theories in \$d\$
dimensions can be described in terms of supergravity (and
string theory) on the product of \$d+1\$-dimensional
\$AdS\$ space with a compact manifold. Here we elaborate on
this idea and propose a precise correspondence between
conformal field theory observables and those of
supergravity: correlation functions in conformal field
theory are given by the dependence of the supergravity
action on the asymptotic behavior at infinity. In
particular, dimensions of operators in conformal field
theory are given by masses of particles in supergravity. As
quantitative confirmation of this correspondence, we note
that the Kaluza-Klein modes of Type IIB supergravity on
\$AdS\_5\times {\bf S}^5\$ match with the chiral operators
of \$\N=4\$ super Yang-Mills theory in four dimensions.
With some further assumptions, one can deduce a Hamiltonian
version of the correspondence and show that the \$\N=4\$
theory has a large \$N\$ phase transition related to the
thermodynamics of \$AdS\$ black holes.},
Archiveprefix = {arXiv},
Author = {Witten, Edward},
Citeulike-Article-Id = {514411},
Citeulike-Linkout-0 = {http://arxiv.org/abs/hep-th/9802150},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/hep-th/9802150},
Date-Added = {2012-06-14 12:26:10 +0530},
Date-Modified = {2012-06-14 12:26:10 +0530},
Day = {6},
Eprint = {hep-th/9802150},
Keywords = {adscft, antidesitter, classic, conformal\_field\_theory, holography, maldacena\_conjecture, supergravity, thermodynamics, witten},
Month = apr,
Posted-At = {2012-06-14 07:55:35},
Priority = {2},
Title = {Anti De Sitter Space And Holography},
Url = {http://arxiv.org/abs/hep-th/9802150},
Year = {1998},
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Bdsk-Url-1 = {http://arxiv.org/abs/hep-th/9802150}}
```

[Bibtex]

```
@article{Natsuume2014AdS/CFT,
Abstract = {{This is the draft version of a textbook on "real-world"
applications of the AdS/CFT duality for beginning graduate
students in particle physics and for researchers in the
other fields. The aim of this book is to provide background
materials such as string theory, general relativity,
nuclear physics, nonequilibrium physics, and
condensed-matter physics as well as some key applications
of the AdS/CFT duality in a single textbook. Contents: (1)
Introduction, (2) General relativity and black holes, (3)
Black holes and thermodynamics, (4) Strong interaction and
gauge theories, (5) The road to AdS/CFT, (6) The AdS
spacetime, (7) AdS/CFT - equilibrium, (8) AdS/CFT - adding
probes, (9) Basics of nonequilibrium physics, (10) AdS/CFT
- nonequilibrium, (11) Other AdS spacetimes, (12)
Applications to quark-gluon plasma, (13) Basics of phase
transition, (14) AdS/CFT - phase transition.}},
Arxiv = {1409.3575},
Author = {Natsuume, Makoto},
Date-Added = {2016-04-13 17:13:12 +0000},
Date-Modified = {2016-04-13 23:02:06 +0530},
File = {FULLTEXT:/home/dvaid/physicistatwork.com/librarian/library/pdfs/01/02031.pdf:PDF},
Title = {{AdS/CFT Duality User Guide}},
Url = {{http://arxiv.org/abs/1409.3575}},
Year = {{2014}},
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Bdsk-Url-1 = {%7Bhttp://arxiv.org/abs/1409.3575%7D}}
```

[Bibtex]

```
@article{McGreevy2010Holographic,
Abstract = {These are notes based on a series of lectures given at the
KITP workshop "Quantum Criticality and the AdS/CFT
Correspondence" in July, 2009. The goal of the lectures was
to introduce condensed matter physicists to the AdS/CFT
correspondence. Discussion of string theory and of
supersymmetry is avoided to the extent possible.},
Archiveprefix = {arXiv},
Author = {McGreevy, John},
Citeulike-Article-Id = {5721860},
Citeulike-Linkout-0 = {http://arxiv.org/abs/0909.0518},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/0909.0518},
Date-Added = {2010-07-04 23:13:29 +0530},
Date-Modified = {2018-12-23 01:50:37 +0530},
Day = {8},
Eprint = {0909.0518},
Keywords = {adscft, holography, lecture\_notes, manybody, quantum\_criticality, review},
Local-Url = {/Users/deepak/ownCloud/root/research/bibdesk/McGreevy.J_Holographic duality with a view toward many-body physics_2010a.pdf},
Month = {May},
Posted-At = {2010-07-04 18:42:55},
Priority = {2},
Title = {Holographic duality with a view toward many-body physics},
Url = {http://arxiv.org/abs/0909.0518},
Year = {2010},
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Bdsk-Url-1 = {http://arxiv.org/abs/0909.0518}}
```

```
@misc{Erdmenger2018Introduction,
Abstract = {We review how the AdS/CFT correspondence is motivated within string theory, and discuss how it is generalized to gauge/gravity duality. In particular, we highlight the relation to quantum information theory by pointing out that the Fisher information metric of a Gaussian probability distribution corresponds to an Anti-de Sitter space. As an application example of gauge/gravity duality, we present a holographic Kondo model. The Kondo model in condensed matter physics describes a spin impurity interacting with a free electron gas: At low energies, the impurity is screened and there is a logarithmic rise of the resistivity. In quantum field theory, this amounts to a negative beta function for the impurity coupling and the theory flows to a non-trivial IR fixed point. For constructing a gravity dual, we consider a large $N$ version of this model in which the ambient electrons are strongly coupled even before the interaction with the impurity is switched on. We present the brane construction which motivates a gravity dual Kondo model and use this model to calculate the impurity entanglement entropy and the resistivity, which has a power-law behaviour. We also study quantum quenches, and discuss the relation to the Sachdev-Ye-Kitaev model.},
Author = {Johanna Erdmenger},
Comments = {37 pages, 13 figures, lectures given at the 2017 TASI Summer School, Boulder, Colorado; conference C17-06-05.4},
Date-Added = {2019-01-01 01:04:58 +0530},
Date-Modified = {2019-01-17 10:40:03 +0530},
Eprint = {arXiv:1807.09872},
Howpublished = {PoS(TASI2017)001},
Title = {{I}ntroduction to {G}auge/{G}ravity {D}uality ({T}{A}{S}{I} {L}ectures 2017)},
Url = {http://arxiv.org/abs/1807.09872},
Year = {2018},
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Bdsk-Url-1 = {http://arxiv.org/abs/1807.09872}}
```

[Bibtex]

```
@article{Sachdev2015Bekenstein-Hawking,
Abstract = {We examine models of fermions with infinite-range
interactions which realize non-Fermi liquids with a
continuously variable U(1) charge density \$\mathcal{Q}\$,
and a non-zero entropy density \$\mathcal{S}\$ at vanishing
temperature. Real time correlators of operators carrying
U(1) charge \$q\$ at a low temperature \$T\$ are
characterized by a \$\mathcal{Q}\$-dependent frequency
\$\omega\_{\mathcal{S}} = (q \, T/\hbar) (\partial
\mathcal{S}/\partial{\mathcal{Q}})\$ which determines a
spectral asymmetry. We show that the correlators match
precisely with those of the AdS\$\_2\$ horizons of extremal
charged black holes. On the black hole side, the matching
employs \$\mathcal{S}\$ as the Bekenstein-Hawking entropy
density, and the laws of black hole thermodynamics which
relate \$(\partial{\mathcal{S}}/\partial{\mathcal{Q}})/(2
\pi)\$ to the electric field strength in AdS\$\_2\$. The
fermion model entropy is computed using the microscopic
degrees of freedom of a UV complete theory without supersymmetry.},
Archiveprefix = {arXiv},
Author = {Sachdev, Subir},
Citeulike-Article-Id = {13763964},
Citeulike-Linkout-0 = {http://arxiv.org/abs/1506.05111},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/1506.05111},
Citeulike-Linkout-2 = {http://dx.doi.org/10.1103/physrevx.5.041025},
Date-Added = {2017-09-05 14:36:21 +0000},
Date-Modified = {2017-09-05 20:06:23 +0530},
Day = {12},
Doi = {10.1103/physrevx.5.041025},
Eprint = {1506.05111},
Issn = {2160-3308},
Journal = {Physical Review X},
Keywords = {ads\_black\_holes, adscft, bekenstein\_hawking\_entropy, correlators, greens\_functions, holography, hubbard\_stratonavich, manybody, non\_fermi\_liquid, quantum\_gravity, sachdev-ye-kitaev, sachdev\_subir, strange\_metals, strongly\_correlated},
Month = aug,
Number = {4},
Posted-At = {2017-09-05 15:36:08},
Priority = {2},
Title = {{Bekenstein-Hawking} Entropy and Strange Metals},
Url = {http://dx.doi.org/10.1103/physrevx.5.041025},
Volume = {5},
Year = {2015},
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Bdsk-Url-1 = {http://dx.doi.org/10.1103/physrevx.5.041025}}
```

[Bibtex]

```
@article{Danshita2017How-to-make,
Abstract = {The realization of quantum field theories on an optical
lattice is an important subject toward the quantum
simulation. We argue that such efforts would lead to the
experimental realizations of quantum black holes. The basic
idea is to construct non-gravitational systems which are
equivalent to the quantum gravitational systems via the
holographic principle. Here the `equivalence' means that
two theories cannot be distinguished even in principle.
Therefore, if the holographic principle is true, one can
create actual quantum black holes by engineering the
non-gravitational systems on an optical lattice. In this
presentation, we consider the simplest example: the
Sachdev-Ye-Kitaev (SYK) model. We design an experimental
scheme for creating the SYK model with use of ultra-cold
fermionic atoms such as Lithium-6.},
Archiveprefix = {arXiv},
Arxivid = {1709.07189},
Author = {Danshita, Ippei and Hanada, Masanori and Tezuka, Masaki},
Date-Added = {2017-09-24 17:46:45 +0000},
Date-Modified = {2017-09-24 23:16:46 +0530},
Eprint = {1709.07189},
File = {:Users/deepak/mendeley/files/Danshita, Hanada, Tezuka{\_}How to make a quantum black hole with ultra-cold gases{\_}2017.pdf:pdf},
Keywords = {analog{\_}gravity,black holes,cold atoms,condensed matter,fermions,holography,lqg,many body,optical lattices,quantum gravity,string{\_}theory,syk model},
Mendeley-Tags = {holography,cold atoms,syk model,quantum gravity,black holes,optical lattices,fermions,analog{\_}gravity,condensed matter,many body,string{\_}theory,lqg},
Month = {sep},
Title = {{How to make a quantum black hole with ultra-cold gases}},
Url = {http://arxiv.org/abs/1709.07189},
Year = {2017},
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Bdsk-Url-1 = {http://arxiv.org/abs/1709.07189}}
```

[Bibtex]

```
@article{Hashimoto2018Imaging,
Abstract = {Clarifying conditions for the existence of a gravitational
picture for a given quantum field theory (QFT) is one of
the fundamental problems in the AdS/CFT correspondence. We
propose a direct way to demonstrate the existence of the
dual black holes: Imaging an Einstein ring. We consider a
response function of the thermal QFT on a two-dimensional
sphere under a time-periodic localized source. The dual
gravity picture, if exists, is a black hole in an
asymptotic global AdS{\$}{\_}4{\$} and a bulk probe field
with a localized source on the AdS boundary. The response
function corresponds to the asymptotic data of the bulk
field propagating in the black hole spacetime. We find a
formula which converts the response function to the image
of the dual black hole: The view of the sky of the AdS bulk
from a point on the boundary. Using the formula, we
demonstrate that, for a thermal state dual to the
Schwarzschild-AdS{\$}{\_}4{\$} spacetime, the Einstein ring
is constructed from the response function. The evaluated
Einstein radius is found to be determined by the total
energy of the dual QFT.},
Archiveprefix = {arXiv},
Arxivid = {1811.12617},
Author = {Hashimoto, Koji and Murata, Keiju and Kinoshita, Shunichiro},
Date-Added = {2018-12-11 11:16:36 +0530},
Date-Modified = {2019-03-12 15:39:53 +0530},
Eprint = {1811.12617},
File = {:Users/deepak/mendeley/Hashimoto, Murata, Kinoshita{\_}Imaging black holes through AdSCFT{\_}2018.pdf:pdf},
Title = {{Imaging black holes through AdS/CFT}},
Url = {https://arxiv.org/abs/1811.12617},
Year = {2018},
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Bdsk-Url-1 = {https://arxiv.org/abs/1811.12617}}
```

- See Sabine’s concise description of the original thought-experiment and of the flaws discovered by Mattingly. ↩