The 23^{th} DAE-BRNS High Energy Physics Symposium was held at IIT Madras from Dec 10 – Dec 14. It was an interesting event. I met lots of very smart people. My abstract based on my paper [1] had been selected for a talk in the “Formal Theory” parallel session on Dec 11. Interestingly the talk preceding mine was delivered by Suresh Govindarajan (INSPIRE) who is a faculty at IITM and a hardcore string theorist. Also in attendance was Prof G. Rajasekaran, who is an emeritus faculty at the Institute of Mathematical Sciences, Chennai and himself a distinguished high energy physicist. Naturally, following Govindarajan’s highly mathematical talk on the existence of BKM superalgebras – of which, I understood perhaps the first three slides – I felt a little trepidatious, especially since the number of mathematical formulae in his talk was several orders of magnitude greater than in mine!

Naveen, a PhD student also from NITK, was kind enough to record my talk on his phone ^{1} . The result is viewable on YouTube.

# Connecting String Theory and LQG

Couple of days later I had a nice conversation with Prof Govindarajan ^{2} where he conveyed to me that the general feeling among many in the strings community was that loops and strings would ultimately have to come together. He mentioned the following questions as his main concerns:

**Matter Degrees of Freedom**

Where is the matter in LQG? In String Theory matter arises “naturally” from compactification of $n>4$ dimensions. The compactified dimensions behave like scalar and gauge fields in the non-compactified geometry. I mentioned to him that LQG does have candidates for matter in the form of topological degrees of freedom known as “preons” [2, 3]. Of course, much work is still to be done to understand how the entire spectrum of the standard model can arise from these topological defects. I made some early efforts trying to connect quantum computation gates and elementary particles in LQG in [4] and to show how non-abelian gauge fields – such as those in the Standard Model – can arise naturally from defects in spin-networks in [5].

**Degenerate geometry in LQG**

Suresh’s next concern was about the existence of geometries in LQG where the tetrad $e_\mu^I$ (which determines the metric geometry via the relation $ g_{\mu\nu} = e_\mu^I e_\nu^J \eta_{IJ}$) is allowed to be degenerate – $\ie~\text{det}(e_\mu^I) = 0$. In such cases the resulting metric exists, however its inverse $g^{\mu\nu}$ does not (because matrices with zero determinant do not have well-defined inverses). His concern might have been motivated by Kaul and Sengupta’s recent work on degenerate spacetimes in the connection formulation of gravity. I explained that there is nothing non-physical about having degenerate spacetimes. One can do all the usual physics with scalars, vectors and spinors in such geometries. However, one also has *new physics* in such regimes which cannot be captured by the metric formulation. In particular with degenerate tetrads one can have geometries with non-zero torsion even without any spinning matter present [6, 7].

**Background dependence of string theory**

String theory as it is usually defined, is a manifestly background dependent theory. Now, presumably a theory of quantum gravity should be background independent. One should be able to extract physical information such as correlation functions, scattering amplitudes and such without having to worry about the background geometry the given processes take place in. Moreover, since in the strong quantum gravity regime, even the gravitational field will be involved in scattering processes, our quantum gravity theory should be able to handle cases which involve transitions between geometries which cannot be treated as perturbations of a given background. Suresh recognizes this shortcoming of String Theory and mentioned it as such to me.

It is in this respect that LQG trumps String Theory. Background independence is manifest and non-negotiable in LQG. We need to be able to incorporate background independence in a meaningful way in the String framework whether it is via String Field Theory or some other approach. LQG can provide pointers on how this might be accomplished.

**Extra dimensions or Lack Thereof**

Extra dimensions are a given in String Theory. The requirement of conformal invariance of the string worldsheet enforces that the spacetime dimensions much be $D = 26$ for the bosonic string and $D = 10$ for the fermionic (or supersymmetric) string. In order to obtain our familiar four dimensional spacetime, these extra dimensions have to be gotten “rid off” in some way. The most method is *compactification* [8, 9] , wherein six (in the case of $D = 10$ superstring theory) dimensions are “rolled up” and only four “large” space+time dimensions remain. The compactified dimensions still manifest physically as effective scalar or gauge fields propagating in the background of the four large dimensions. These extra dimensions are also the source of much criticism of String Theory. It turns out that there is a huge ($\sim 10^{500}$ ways in which the extra dimensions can be compactified and which one of these, if any, compactifications can give rise to our Universe with the Standard Model and all its interactions is a notoriously intractable problem.

Extra dimensions are not present, and in fact are not needed, in Loop Quantum Gravity. This is considered a net plus for LQG. However the optimism might be short-lived. All those extra dimensions in String Theory, which seem like so much clutter, can actually be used to produce experimentally verifiable predictions about QCD scattering processes! Sakai and Sugimoto [10] first initiated this approach by constructing a holographic dual of large-N QCD. Following this work many authors, including Aalok Misra and his brilliant student Vikas Yadav, whom I had the pleasure of meeting at this conference, have managed to use the Sakai-Sugimoto framework to predict decay widths of glueballs [11] (bound states of gluons) which appear to match very nicely with lattice QCD calculations. LQG is yet to deliver on any such quantitive particle physics related predictions, though it does have several predictions on the astrophysical front [12, 13, 14], which if confirmed would be a stunning success.

# Noncommutative Geometry and Preons

Another very interesting talk was delivered by Prof. Rajiv Gavai from TIFR on work [15] done with Pulkit Ghoderao and P. Ramadevi, on the possible detection of non-commutative effects by measuring the Lamb shift of the hydrogen atom or in accelerator experiments. Two mathematical quantities $A, B$ are said to be “non-commutative” (or “non-commuting” or “do not commute”), when they *dont’* satisfy the following relation:

$$ [A,B] = 0 $$

where $ [A,B] = AB – BA $ is referred to as the “commutator”. Experts may skip the following subsection.

## Non-commutativity for Non-Experts

A trivial example is any pair of complex numbers $ z_1, z_2 $. Using the rules of complex multiplication one can easily see that $ [z_1, z_2] = 0$ for all $z_1, z_2 \in \mathbb{C}$. This is also obviously also true for all real numbers which are a subset of the complex numbers. However, this is not true for quaternions and octonions, which along with the real and complex numbers, constitute the only four normed division algebras (see for e.g. [16]) possible mathematically. It is also not true, in general, for matrices. One can see this by taking any two $ 2 \times 2$ matrices with random elements and calculating the commutator.

Another example is given by operators in quantum theory. Position $x$ and momentum $p$ are represented by operators $ \hat x$ and $\hat p$, respectively. While the classical variables commute: $ { x, p } = 0$ ^{3}, their operator versions don’t: $[ \hat x, \hat p] = i\hbar \ne 0 $. In this sense, the phase space of a quantum mechanical system is an example of a non-commutative geometry.

The non-commutativity Ghoderao et al.’s work is concerned with is between different spatial co-ordinates:

$$ [x_i, x_j] = i \theta_{ij} $$

where $\theta_{ij}$ measures the *amount* of non-commutativity. Now this is very interesting. For instance, if you consider a particle in a plane, the operation $ x y$ correspond to walking one unit in the $y$ direction, followed by one unit in the $x$ direction. $ y x$ is defined in the same way. Now, normally we expect that both operations should get us to the same point, $\ie$ $ xy = yx$. However, if we were living on a non-commutative plane then this would no longer be true. In a sense, non-commutativity measures the presence of “non-abelian defects” in geometry. Both String Theory and LQG generically predict non-commutative effects arising from quantum geometry. Thus the existence of such an effect would provide very strong support for both theories and also allow us to differentiate between various models.

## Composite Particles and Non-commutativity

Ghoderao et al’s result can be summarized in one sentence

in a non-commutative geometry, quarks can form composite particles such as protons and neutrons, if and only if, they (quarks) have substructure.

Now this is a stunning result which also applies to leptons such as electrons, muons and neutrinos. The reason I found this work particularly exciting is because it provides very strong circumstantial evidence for the *preon model* of elementary particles developed by my good friend and collaborator Sundance Bilson-Thompson [2] ^{4}. This model predicts precisely such a substructure for the leptons and quarks. It would be very interesting to try to understand the relationship between the Bilson-Thompson model and non-commutative geometry.

# Fermi Arcs and AdS/CFT

Finally, there was very interesting work presented by Wadbor Wahlang who is a graduate student working under Sayan Chakrabarti at IIT Guwahati. This work was about understanding the origin of Fermi arcs in Weyl semi-metals ^{5} from a holographic perspective.

As is well understood by now [17, 18, 19] the AdS/CFT correspondence can be used to explore the phase diagram of condensed matter systems. Essentially what Wahlang and Chakrabarti do is to couple free fermion fields to the usual scalar field living in the bulk AdS spacetime and use that to calculate the spectral function of the boundary field theory. In the event that the fermionic fields they use are Weyl fermions, the spectral function exhibits Fermi arcs. I am looking forward to seeing this work on the arXiv.

- It might seem a bit narcissistic to some to record one’s own conference talks. However, for scientists, talks are the best way to communicate our ideas to our own community and to the general public. They also serve to help us improve our presentation skills. There’s really no downside to recording your own talks, except perhaps the realization that you’re not quite as slim as you’d like to imagine. ↩
- This version is only my recollection of my conversation with Prof Govindarajan and has not been endorsed or approved by him. Any errors or omissions are solely mine. ↩
- We are using curly braces ${,}$ because in classical mechanics the commutator is given by the Poisson bracket which is written in this way, whereas square braces $[,]$ are typically used to represent commutators of quantum mechanical quantities. ↩
- Just to clarify, I met Sundance long after he had discovered the “Bilson-Thompson” mode and I had no role in its discovery. I did try to explain how it could be embedded into LQG in [3] ↩
- See, for $\eg$ [20] for an introduction to the concept of Weyl fermions, Weyl semi-metals and Fermi arcs. ↩

[Bibtex]

```
@article{Vaid2017Connecting,
Abstract = {We argue that String Theory and Loop Quantum Gravity can
be thought of as describing different regimes of a single
unified theory of quantum gravity. LQG can be thought of as
providing the pre-geometric exoskeleton out of which
macroscopic geometry emerges and String Theory then becomes
the $\backslash$emph{\{}effective{\}} theory which
describes the dynamics of that exoskeleton. The core of the
argument rests on the claim that the Nambu-Goto action of
String Theory can be viewed as the expectation value of the
LQG area operator evaluated on the string worldsheet.},
Archiveprefix = {arXiv},
Arxivid = {1711.05693},
Author = {Vaid, Deepak},
Date-Added = {2018-01-09 16:38:35 +0000},
Date-Modified = {2018-01-09 22:08:37 +0530},
Eprint = {1711.05693},
File = {:Users/deepak/mendeley/files/Vaid{\_}Connecting Loop Quantum Gravity and String Theory via Quantum Geometry{\_}2017(2).pdf:pdf},
Keywords = {area operator,conformal invariance,loop quantum gravity,nambu-goto action,quantum gravity,string theory,vaid{\_}deepak},
Mendeley-Tags = {vaid{\_}deepak,string theory,loop quantum gravity,area operator,conformal invariance,nambu-goto action,quantum gravity},
Month = {nov},
Title = {{Connecting Loop Quantum Gravity and String Theory via Quantum Geometry}},
Url = {http://arxiv.org/abs/1711.05693},
Year = {2017},
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Bdsk-Url-1 = {http://arxiv.org/abs/1711.05693}}
```

[Bibtex]

```
@article{Vaid2010Embedding,
Abstract = {We argue that the Quadratic Spinor Lagrangian approach
allows us to approach the problem of forming a geometrical
condensate of spinorial tetrads in a natural manner. This,
along with considerations involving the discrete symmetries
of lattice triangulations, lead us to discover that the
quasiparticles of such a condensate are tetrahedra with
braids attached to its faces and that these braid
attachments correspond to the preons in Bilson-Thompson's
model of elementary particles. These "spatoms" can then be
put together in a tiling to form more complex structures
which encode both geometry and matter in a natural manner.
We conclude with some speculations on the relation between
this picture and the computational universe hypothesis.},
Archiveprefix = {arXiv},
Author = {Vaid, Deepak},
Citeulike-Article-Id = {7265311},
Citeulike-Linkout-0 = {http://arxiv.org/abs/1002.1462},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/1002.1462},
Date-Added = {2010-06-08 04:38:44 +0530},
Date-Modified = {2010-06-08 04:38:45 +0530},
Day = {8},
Eprint = {1002.1462},
Keywords = {bilson-thompson, braids, computational\_universe, condensate, defects, elementary\_particles, quadratic-spinor-lagrangian, quantum\_gravity, standard\_model, topology},
Month = {Feb},
Posted-At = {2010-06-08 00:08:18},
Priority = {2},
Title = {Embedding the Bilson-Thompson model in an LQG-like framework},
Url = {http://arxiv.org/abs/1002.1462},
Year = {2010},
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Bdsk-Url-1 = {http://arxiv.org/abs/1002.1462}}
```

```
@misc{Vaid2013Elementary,
Abstract = {It is shown that there exists a mapping between the
fermions of the Standard Model ({SM}) represented as braids
in the {Bilson-Thompson} model, and a set of gates which
can perform Universal Quantum Computation ({UQC}). This
leads us to conjecture that the "Computational Universe
Hypothesis" ({CUH}) can be given a concrete implementation
in a new physical framework where elementary particles and
the gauge bosons (which intermediate interactions between
fermions) are interpreted as the components of a quantum
computational network, with the particles serving as
quantum computational gates and the gauge fields as the
information carrying entities.},
Archiveprefix = {arXiv},
Author = {Vaid, Deepak},
Citeulike-Article-Id = {12456844},
Citeulike-Linkout-0 = {http://arxiv.org/abs/1307.0096},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/1307.0096},
Date-Added = {2013-07-02 10:13:59 +0530},
Date-Modified = {2013-07-02 10:14:01 +0530},
Day = {29},
Eprint = {1307.0096},
Keywords = {bilson-thompson, braids, computational\_universe, fqxi, large\_gauge\_transformation, lqg, preons, quantum\_computation, quantum\_gates, quantum\_gravity, universal, vaid\_d},
Month = jun,
Posted-At = {2013-07-02 05:42:42},
Priority = {2},
Title = {Elementary Particles as Gates for Universal Quantum Computation},
Url = {http://arxiv.org/abs/1307.0096},
Year = {2013},
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Bdsk-Url-1 = {http://arxiv.org/abs/1307.0096}}
```

```
@misc{Vaid2013Non-abelian,
Abstract = {\emph{Effective} gauge fields arise in the description of
the dynamics of defects in lattices of graphene in
condensed matter. The interactions between neighboring
nodes of a lattice/spin-network are described by the
Hubbard model whose effective field theory at long
distances is given by the Dirac equation for an
\emph{emergent} gauge field. The spin-networks in question
can be used to describe the geometry experienced by a
non-inertial observer in flat spacetime moving at a
constant acceleration in a given direction. We expect such
spin-networks to describe the structure of quantum horizons
of black holes in loop quantum gravity. We argue that the
abelian and non-abelian gauge fields of the Standard Model
can be identified with the emergent degrees of freedom
required to describe the dynamics of defects in symmetry
reduced spin-networks.},
Archiveprefix = {arXiv},
Author = {Vaid, Deepak},
Citeulike-Article-Id = {12605949},
Citeulike-Linkout-0 = {http://arxiv.org/abs/1309.0652},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/1309.0652},
Date-Added = {2013-09-04 12:11:57 +0530},
Date-Modified = {2013-09-04 12:12:01 +0530},
Day = {3},
Eprint = {1309.0652},
Keywords = {condensed\_matter, emergence, gauge\_fields, graphene, horizons, lqg, manybody, quantum\_gravity, symmetry\_reduction, vaid\_d},
Month = sep,
Posted-At = {2013-09-04 07:38:52},
Priority = {2},
Title = {Non-abelian Gauge Fields from Defects in {Spin-Networks}},
Url = {http://arxiv.org/abs/1309.0652},
Year = {2013},
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Bdsk-Url-1 = {http://arxiv.org/abs/1309.0652}}
```

[Bibtex]

```
@article{Kaul2016Degenerate,
Abstract = {We present a systematic framework to obtain the most
general solutions of the equations of motion in first order
gravity theory with degenerate tetrads. There are many
possible solutions. Generically, these exhibit
non-vanishing torsion even in the absence of any matter
coupling. These solutions are shown to contain a special
set of eight configurations which are associated with the
homogeneous model three-geometries of Thurston.},
Archiveprefix = {arXiv},
Arxivid = {1602.04559},
Author = {Kaul, Romesh K. and Sengupta, Sandipan},
Date-Added = {2018-12-19 13:54:18 +0530},
Date-Modified = {2018-12-19 13:54:23 +0530},
Doi = {10.1103/PhysRevD.93.084026},
Eprint = {1602.04559},
File = {:Users/deepak/ownCloud/root/research/mendeley/Kaul, Sengupta{\_}Degenerate spacetimes in first order gravity{\_}2016.pdf:pdf},
Issn = {2470-0010},
Journal = {Physical Review D},
Month = {feb},
Number = {8},
Pages = {084026},
Title = {{Degenerate spacetimes in first order gravity}},
Url = {https://link.aps.org/doi/10.1103/PhysRevD.93.084026 http://arxiv.org/abs/1602.04559 http://dx.doi.org/10.1103/PhysRevD.93.084026},
Volume = {93},
Year = {2016},
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Bdsk-Url-1 = {https://link.aps.org/doi/10.1103/PhysRevD.93.084026%20http://arxiv.org/abs/1602.04559%20http://dx.doi.org/10.1103/PhysRevD.93.084026},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevD.93.084026}}
```

[Bibtex]

```
@article{Kaul2016New-solutions,
Abstract = {In first order formulation of pure gravity, we find a new
class of solutions to the equations of motion represented
by degenerate four-geometries. These configurations are
described by non- invertible tetrads with two zero
eigenvalues and admit non-vanishing torsion. The
homogeneous ones among these infinitely many degenerate
solutions admit a geometric classification provided by the
three fundamental geometries that a closed two-surface can
accomodate, namely, E{\^{}}2 , S{\^{}}2 and H{\^{}}2.},
Archiveprefix = {arXiv},
Arxivid = {1609.02344},
Author = {Kaul, Romesh K. and Sengupta, Sandipan},
Date-Added = {2018-12-19 13:54:18 +0530},
Date-Modified = {2018-12-19 13:54:23 +0530},
Doi = {10.1103/PhysRevD.94.104047},
Eprint = {1609.02344},
File = {:Users/deepak/ownCloud/root/research/mendeley/Kaul, Sengupta{\_}New solutions in pure gravity with degenerate tetrads{\_}2016.pdf:pdf},
Issn = {24700029},
Journal = {Physical Review D},
Number = {10},
Title = {{New solutions in pure gravity with degenerate tetrads}},
Volume = {94},
Year = {2016},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {https://doi.org/10.1103/PhysRevD.94.104047}}
```

[Bibtex]

```
@article{Kawai1986Construction,
Abstract = {We present a simple set of rules for constructing
ultraviolet-finite closed-fermionic-string models. In
particular, the method easily gives four-dimensional models
which possess N=1 super-symmetry, chiral fermions, and
phenomenologically interesting gauge groups.},
Author = {Kawai, Hikaru and Lewellen, David C. and Tye, S. Henry H.},
Citeulike-Article-Id = {11128140},
Citeulike-Linkout-0 = {http://dx.doi.org/10.1103/PhysRevLett.57.1832},
Citeulike-Linkout-1 = {http://link.aps.org/abstract/PRL/v57/i15/p1832},
Citeulike-Linkout-2 = {http://link.aps.org/pdf/PRL/v57/i15/p1832},
Date-Added = {2012-08-24 18:37:10 +0530},
Date-Modified = {2012-08-24 18:39:50 +0530},
Doi = {10.1103/PhysRevLett.57.1832},
Journal = {Physical Review Letters},
Keywords = {4d, classic, closed\_strings, compactification, fermions, kawai\_h, lewellen\_d, phenomenology, prl, string\_theory, supersymmetry, tye\_s},
Month = oct,
Pages = {1832--1835},
Posted-At = {2012-08-24 14:01:49},
Priority = {2},
Publisher = {American Physical Society},
Title = {Construction of {Four-Dimensional} Fermionic String Models},
Url = {http://dx.doi.org/10.1103/PhysRevLett.57.1832},
Volume = {57},
Year = {1986},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://dx.doi.org/10.1103/PhysRevLett.57.1832}}
```

[Bibtex]

```
@article{Kawai1987Construction,
Abstract = {The construction of four-dimensional closed fermionic
string models is discussed. The approach is based on a
fermionic formulation of all internal (i.e. toroidally
compactified) coordinates. Modular invariance, world sheet
supersymmetry, (super)conformal invariance and proper
space-time spin-statistics impose stringent constraints on
the model building. Using these constraints on the boundary
conditions (spin structure) of the world sheet fermions, we
obtain a simple set of rules for constructing
ultraviolet-finite closed fermionic string models. For a
large subclass of these models, this '' spin structure''
construction can be related to bosonic constructions via
the fermionic charge lattice. These charge lattices are odd
lorentzian self-dual lattices shifted by a fixed vector and
form a nontrivial generalization of the lorentzian
self-dual even-integer lattices considered by Narian. In
particular, four-dimensional models with N = 4, N = 2, and
N = 1 supersymmetry as well as non-supersymmetric
tachyon-free chiral models can easily be construted. Some
models may be interpreted as charge lattices moded by
discrete symmetries - in particular Z2 type orbifolds.
String interactions and other related issues are also
discussed.},
Author = {Kawai, Hikaru and Lewellen, David C. and Henry Tye, S. H.},
Citeulike-Article-Id = {11128049},
Citeulike-Linkout-0 = {http://dx.doi.org/10.1016/0550-3213(87)90208-2},
Date-Added = {2012-08-24 18:36:42 +0530},
Date-Modified = {2012-08-24 18:39:50 +0530},
Doi = {10.1016/0550-3213(87)90208-2},
Issn = {05503213},
Journal = {Nuclear Physics B},
Keywords = {4d, classic, closed\_strings, compactification, fermions, kawai\_h, lattice\_models, lewellen\_d, phenomenology, string\_theory, supersymmetry, tye\_s},
Month = jan,
Pages = {1--76},
Posted-At = {2012-08-24 14:04:15},
Priority = {2},
Title = {Construction of fermionic string models in four dimensions},
Url = {http://dx.doi.org/10.1016/0550-3213(87)90208-2},
Volume = {288},
Year = {1987},
Bdsk-File-1 = {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},
Bdsk-Url-1 = {http://dx.doi.org/10.1016/0550-3213(87)90208-2}}
```

[Bibtex]

```
@article{Sakai2005Low-Energy,
Abstract = {We present a holographic dual of four-dimensional, large
N{\_}c QCD with massless flavors. This model is constructed
by placing N{\_}f probe D8-branes into a D4 background,
where supersymmetry is completely broken. The chiral
symmetry breaking in QCD is manifested as a smooth
interpolation of D8 - anti-D8 pairs in the supergravity
background. The meson spectrum is examined by analyzing a
five-dimensional Yang-Mills theory that originates from the
non-Abelian DBI action of the probe D8-brane. It is found
that our model yields massless pions, which are identified
with Nambu-Goldstone bosons associated with the chiral
symmetry breaking. We obtain the low-energy effective
action of the pion field and show that it contains the
usual kinetic term of the chiral Lagrangian and the Skyrme
term. A brane configuration that defines a dynamical baryon
is identified with the Skyrmion. We also derive the
effective action including the lightest vector meson. Our
model is closely related to that in the hidden local
symmetry approach, and we obtain a
Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin-type relation
among the couplings. Furthermore, we investigate the
Chern-Simons term on the probe brane and show that it leads
to the Wess-Zumino-Witten term. The mass of the
$\backslash$eta' meson is also considered, and we formulate
a simple derivation of the $\backslash$eta' mass term
satisfying the Witten-Veneziano formula from supergravity.},
Archiveprefix = {arXiv},
Arxivid = {hep-th/0412141},
Author = {Sakai, Tadakatsu and Sugimoto, Shigeki},
Date-Added = {2018-12-16 00:27:09 +0530},
Date-Modified = {2018-12-16 00:27:10 +0530},
Doi = {10.1143/PTP.113.843},
Eprint = {0412141},
File = {:Users/deepak/mendeley/Sakai, Sugimoto{\_}Low Energy Hadron Physics in Holographic QCD{\_}2005.pdf:pdf},
Isbn = {0033-068X},
Issn = {0033-068X},
Journal = {Progress of Theoretical Physics},
Mendeley-Groups = {AdS/CFT,Hadron Masses from Quantum Groups},
Month = {apr},
Number = {4},
Pages = {843--882},
Primaryclass = {hep-th},
Title = {{Low Energy Hadron Physics in Holographic QCD}},
Url = {http://arxiv.org/abs/hep-th/0412141 http://dx.doi.org/10.1143/PTP.113.843 http://arxiv.org/abs/hep-th/0412141{\%}0Ahttp://dx.doi.org/10.1143/PTP.113.843 https://academic.oup.com/ptp/article-lookup/doi/10.1143/PTP.113.843},
Volume = {113},
Year = {2005},
Bdsk-Url-1 = {https://doi.org/10.1143/PTP.113.843}}
```

[Bibtex]

```
@article{Yadav2018M-theory,
Abstract = {Using the pull-back of the perturbed type IIA metric
corresponding to the perturbation of
arXiv:hep-th/1306.4339's M-theory uplift of
arXiv:hep-th/0902.1540's UV-complete top-down type IIB
holographic dual of large-{\$}N{\$} thermal QCD, at finite
coupling, we obtain the interaction Lagrangian
corresponding to exotic scalar
glueball({\$}G{\_}E{\$})-{\$}\backslashrho/\backslashpi{\$}-meson
interaction, linear in the exotic scalar glueball and up to
quartic order in the {\$}\backslashpi{\$} mesons. In the
Lagrangian, the coupling constants are determined as
(radial integrals of) arXiv:hep-th/1306.4339's M-theory
uplift's metric components and six radial functions
appearing in the M-theory metric perturbations. Assuming
{\$}M{\_}G{\textgreater}2M{\_}\backslashrho{\$}, we then
compute {\$}\backslashrho\backslashrightarrow2\backslashpi,
G{\_}E\backslashrightarrow2\backslashpi, 2\backslashrho,
\backslashrho+2\backslashpi{\$} decay widths as well as the
direct and indirect (mediated via {\$}\backslashrho{\$}
mesons) {\$}G{\_}E\backslashrightarrow4\backslashpi{\$}
decays. For numerics, we choose {\$}f0[1710]{\$} and
compare with previous calculations. We emphasize that our
results can be made to match PDG data (and improvements
thereof) exactly by appropriate tuning of some constants of
integration appearing in the solution of the M-theory
metric perturbations and the {\$}\backslashrho{\$} and
{\$}\backslashpi{\$} meson radial profile functions - a flexibility that our calculations permits.},
Archiveprefix = {arXiv},
Arxivid = {1808.01182},
Author = {Yadav, Vikas and Misra, Aalok},
Date-Added = {2018-12-16 00:27:09 +0530},
Date-Modified = {2018-12-16 00:27:10 +0530},
Doi = {10.1007/JHEP09(2018)133},
Eprint = {1808.01182},
File = {:Users/deepak/mendeley/Yadav, Misra{\_}M-Theory Exotic Scalar Glueball Decays to Mesons at Finite Coupling{\_}2018.pdf:pdf},
Issn = {1029-8479},
Journal = {Journal of High Energy Physics},
Mendeley-Groups = {AdS/CFT},
Month = {sep},
Number = {9},
Pages = {133},
Title = {{M-theory exotic scalar glueball decays to mesons at finite coupling}},
Url = {http://arxiv.org/abs/1808.01182 http://dx.doi.org/10.1007/JHEP09(2018)133 http://arxiv.org/abs/1808.01182{\%}0Ahttp://dx.doi.org/10.1007/JHEP09(2018)133 http://link.springer.com/10.1007/JHEP09(2018)133},
Volume = {2018},
Year = {2018},
Bdsk-Url-1 = {https://doi.org/10.1007/JHEP09(2018)133}}
```

```
@misc{Rovelli2014Planck,
Abstract = {A star that collapses gravitationally can reach a further
stage of its life, where quantum-gravitational pressure
counteracts weight. The duration of this stage is very
short in the star proper time, yielding a bounce, but
extremely long seen from the outside, because of the huge
gravitational time dilation. Since the onset of
quantum-gravitational effects is governed by energy density
--not by size-- the star can be much larger than planckian
in this phase. The object emerging at the end of the
Hawking evaporation of a black hole can can then be larger
than planckian by a factor \$(m/m\_{\scriptscriptstyle
P})^n\$, where \$m\$ is the mass fallen into the hole,
\$m\_{\scriptscriptstyle P}\$ is the Planck mass, and \$n\$
is positive. The existence of these objects alleviates the
black-hole information paradox. More interestingly, these
objects could have astrophysical and cosmological interest:
they produce a detectable signal, of quantum gravitational
origin, around the \$10^{-14} cm\$ wavelength.},
Archiveprefix = {arXiv},
Author = {Rovelli, Carlo and Vidotto, Francesca},
Citeulike-Article-Id = {12939852},
Citeulike-Linkout-0 = {http://arxiv.org/abs/1401.6562},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/1401.6562},
Date-Added = {2014-01-28 11:30:26 +0000},
Date-Modified = {2014-01-28 17:00:30 +0530},
Day = {25},
Eprint = {1401.6562},
Keywords = {cosmology, gravitational\_collapse, observational, prediction, quantum\_bounce, quantum\_gravity, rovelli, singularity, star, vidotto\_francesca},
Month = jan,
Posted-At = {2014-01-28 11:29:20},
Priority = {2},
Title = {Planck stars},
Url = {http://arxiv.org/abs/1401.6562},
Year = {2014},
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Bdsk-Url-1 = {http://arxiv.org/abs/1401.6562}}
```

[Bibtex]

```
@article{Barrau2014Fast,
Abstract = {We estimate the size of a primordial black hole exploding
today via a white hole transition, and the power in the
resulting explosion, using a simple model. We point out
that Fast Radio Bursts, strong signals with millisecond
duration, probably extragalactic and having unknown source,
have wavelength not far from the expected size of the
exploding hole. We also discuss the possible higher energy
components of the signal.},
Archiveprefix = {arXiv},
Arxivid = {1409.4031},
Author = {Barrau, Aur{\'{e}}lien and Rovelli, Carlo and Vidotto, Francesca},
Date-Added = {2018-01-13 09:15:52 +0000},
Date-Modified = {2018-01-13 14:45:54 +0530},
Doi = {10.1103/PhysRevD.90.127503},
Eprint = {1409.4031},
File = {:Users/deepak/mendeley/files/Barrau, Rovelli, Vidotto{\_}Fast radio bursts and white hole signals{\_}2014.pdf:pdf},
Issn = {15502368},
Journal = {Physical Review D - Particles, Fields, Gravitation and Cosmology},
Number = {12},
Title = {{Fast radio bursts and white hole signals}},
Url = {http://arxiv.org/abs/1409.4031 http://dx.doi.org/10.1103/PhysRevD.90.127503 https://arxiv.org/abs/1409.4031},
Volume = {90},
Year = {2014},
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Bdsk-Url-2 = {https://dx.doi.org/10.1103/PhysRevD.90.127503}}
```

[Bibtex]

```
@article{Barrau2017Bouncing,
Abstract = {Non-perturbative quantum-gravity effects can change the
fate of black holes and make them bounce in a time scale
shorter than the Hawking evaporation time. In this article,
we show that this hypothesis can account for the GeV excess
observed from the galactic center by the Fermi satellite.
By carefully taking into account the secondary component
due to the decay of unstable hadrons, we show that the
model is fully self-consistent. This phenomenon presents a
specific redshift-dependence that could allow to
distinguish it from other astrophysical phenomena possibly
contributing to the GeV excess.},
Archiveprefix = {arXiv},
Arxivid = {1606.08031},
Author = {Barrau, Aur{\'{e}}lien and Bolliet, Boris and Schutten, Marrit and Vidotto, Francesca},
Date-Added = {2018-10-28 22:18:10 +0530},
Date-Modified = {2018-10-28 22:18:12 +0530},
Doi = {10.1016/j.physletb.2017.05.040},
Eprint = {1606.08031},
File = {:Users/deepak/mendeley/Barrau et al.{\_}Bouncing black holes in quantum gravity and the Fermi gamma-ray excess{\_}2017.pdf:pdf},
Isbn = {8392233778},
Issn = {03702693},
Journal = {Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics},
Mendeley-Groups = {Black Hole Evaporation},
Month = {jun},
Pages = {58--62},
Title = {{Bouncing black holes in quantum gravity and the Fermi gamma-ray excess}},
Url = {http://arxiv.org/abs/1606.08031 http://dx.doi.org/10.1016/j.physletb.2017.05.040},
Volume = {772},
Year = {2017},
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Bdsk-Url-1 = {http://arxiv.org/abs/1606.08031%20http://dx.doi.org/10.1016/j.physletb.2017.05.040},
Bdsk-Url-2 = {https://doi.org/10.1016/j.physletb.2017.05.040}}
```

[Bibtex]

```
@article{Ghoderao2018Probing,
Abstract = {Examining quantum electrodynamics in non-commutative (NC)
spaces along with composite operators in these spaces, we
show that i) any charge g for a fermion matter field is
allowed provided the basic NC photon-photon coupling is g,
however no other multiples of g are permitted and ii)
composite operators do not have a simple transformation
which can be attributed to the effective total charge of
the composite particle. Taken together these results place
a limit on the scale of non-commutativity to be at most
smaller that current LHC limits for compositeness.
Furthermore, they also suggest that a substructure at still
smaller scales is needed if such spaces are to be a
physical reality.},
Archiveprefix = {arXiv},
Arxivid = {1806.06015},
Author = {Ghoderao, Pulkit S. and Gavai, Rajiv V. and Ramadevi, P.},
Date-Added = {2018-12-13 11:04:48 +0530},
Date-Modified = {2018-12-13 11:04:49 +0530},
Eprint = {1806.06015},
File = {:Users/deepak/mendeley/Ghoderao, Gavai, Ramadevi{\_}Probing the scale of non-commutativity of space{\_}2018.pdf:pdf},
Mendeley-Groups = {Preons and Standard Model,Hadron Masses from Quantum Groups},
Month = {jun},
Title = {{Probing the scale of non-commutativity of space}},
Url = {http://arxiv.org/abs/1806.06015},
Year = {2018},
Bdsk-Url-1 = {http://arxiv.org/abs/1806.06015}}
```

[Bibtex]

```
@article{Baez2002The-Octonions,
Abstract = {The octonions are the largest of the four normed division
algebras. While somewhat neglected due to their
nonassociativity, they stand at the crossroads of many
interesting fields of mathematics. Here we describe them
and their relation to Clifford algebras and spinors, Bott
periodicity, projective and Lorentzian geometry, Jordan
algebras, and the exceptional Lie groups. We also touch
upon their applications in quantum logic, special
relativity and supersymmetry.},
Archiveprefix = {arXiv},
Author = {Baez, John C.},
Citeulike-Article-Id = {820312},
Citeulike-Linkout-0 = {http://arxiv.org/abs/math.RA/0105155},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/math.RA/0105155},
Date-Added = {2011-04-22 20:13:02 +0530},
Date-Modified = {2011-04-22 20:13:03 +0530},
Day = {23},
Eprint = {math.RA/0105155},
Keywords = {baez, geometry, mathematical\_physics, octonions, pedagogical, physics},
Month = apr,
Posted-At = {2011-04-22 15:42:37},
Priority = {2},
Title = {The Octonions},
Url = {http://arxiv.org/abs/math.RA/0105155},
Year = {2002},
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Bdsk-Url-1 = {http://arxiv.org/abs/math.RA/0105155}}
```

[Bibtex]

```
@article{Hartnoll2010Lectures,
Abstract = {These notes are loosely based on lectures given at the
CERN Winter School on Supergravity, Strings and Gauge
theories, February 2009 and at the IPM String School in
Tehran, April 2009. I have focused on a few concrete topics
and also on addressing questions that have arisen
repeatedly. Background condensed matter physics material is
included as motivation and easy reference for the high
energy physics community. The discussion of holographic
techniques progresses from equilibrium, to transport and to
superconductivity.},
Archiveprefix = {arXiv},
Author = {Hartnoll, Sean A.},
Citeulike-Article-Id = {4196751},
Citeulike-Linkout-0 = {http://arxiv.org/abs/0903.3246},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/0903.3246},
Citeulike-Linkout-2 = {http://dx.doi.org/10.1088/0264-9381/26/22/224002},
Date-Added = {2010-04-09 04:40:59 +0530},
Date-Modified = {2018-12-23 01:41:22 +0530},
Day = {17},
Doi = {10.1088/0264-9381/26/22/224002},
Eprint = {0903.3246},
Keywords = {condensed\_matter, holography, lecture-notes, transport-coefficients},
Local-Url = {/Users/deepak/ownCloud/root/research/bibdesk/Hartnoll.S_Lectures on holographic methods for condensed matter physics_2010a.pdf},
Month = {Jan},
Priority = {2},
Title = {Lectures on holographic methods for condensed matter physics},
Url = {http://dx.doi.org/10.1088/0264-9381/26/22/224002},
Year = {2010},
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Bdsk-Url-1 = {http://dx.doi.org/10.1088/0264-9381/26/22/224002}}
```

[Bibtex]

```
@article{Hartnoll2008Holographic,
Abstract = {It has been shown that a gravitational dual to a
superconductor can be obtained by coupling anti-de Sitter
gravity to a Maxwell field and charged scalar. We review
our earlier analysis of this theory and extend it in two
directions. First, we consider all values for the charge of
the scalar field. Away from the large charge limit,
backreaction on the spacetime metric is important. While
the qualitative behaviour of the dual superconductor is
found to be similar for all charges, in the limit of
arbitrarily small charge a new type of black hole
instability is found. We go on to add a perpendicular
magnetic field B and obtain the London equation and
magnetic penetration depth. We show that these holographic
superconductors are Type {II}, i.e., starting in a normal
phase at large B and low temperatures, they develop
superconducting droplets as B is reduced.},
Archiveprefix = {arXiv},
Author = {Hartnoll, Sean A. and Herzog, Christopher P. and Horowitz, Gary T.},
Citeulike-Article-Id = {3507541},
Citeulike-Linkout-0 = {http://arxiv.org/abs/0810.1563},
Citeulike-Linkout-1 = {http://arxiv.org/pdf/0810.1563},
Date-Added = {2011-06-18 14:16:20 +0530},
Date-Modified = {2011-06-18 14:16:20 +0530},
Day = {9},
Eprint = {0810.1563},
Keywords = {adscft, antidesitter, condensate, duality, holography, review, superconductivity},
Month = oct,
Posted-At = {2011-06-18 09:45:30},
Priority = {2},
Title = {Holographic Superconductors},
Url = {http://arxiv.org/abs/0810.1563},
Year = {2008},
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Bdsk-Url-1 = {http://arxiv.org/abs/0810.1563}}
```

[Bibtex]

```
@article{Hartman2010Cooper,
Abstract = {We show that a quartic contact interaction between charged
fermions can lead to Cooper pairing and a superconducting
instability in the background of a charged asymptotically
Anti-de Sitter black hole. For a massless fermion we obtain
the zero mode analytically and compute the dependence of
the critical temperature T_c on the charge of the fermion.
The instability we find occurs at charges above a critical
value, where the fermion dispersion relation near the Fermi
surface is linear. The critical temperature goes to zero as
the marginal Fermi liquid is approached, together with the
density of states at the Fermi surface. Besides the charge,
the critical temperature is controlled by a four point
function of a fermionic operator in the dual strongly
coupled field theory.},
Author = {Hartman, Thomas and Hartnoll, Sean A.},
Date-Added = {2015-09-03 08:07:16 +0000},
Date-Modified = {2015-09-03 13:37:21 +0530},
Doi = {10.1007/JHEP06(2010)005},
File = {FULLTEXT:/home/dvaid/physicistatwork.com/librarian/library/02197.pdf:PDF},
Journal = {JHEP 1006:005,2010},
Title = {Cooper pairing near charged black holes},
Url = {http://arxiv.org/abs/1003.1918},
Year = {2010},
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```

[Bibtex]

```
@article{Rao2016Weyl,
Abstract = {We begin this review with an introduction and a discussion
of Weyl fermions as emergent particles in condensed matter
systems, and explain how high energy phenomena like the
chiral anomaly can be seen in low energy experiments. We
then explain the current interest in the field due to the
recent discovery of real materials which behave like Weyl
semi-metals. We then describe a simple lattice model of a
topological insulator, which can be turned into a Weyl
semi-metal on breaking either time-reversal or inversion
symmetry, and show how flat bands or Fermi arcs develop.
Finally, we describe some new phenomena which occur due to
the chiral nature of the Weyl nodes and end with possible
future prospects in the field, both in theory and
experiment.},
Annote = {arXiv: 1603.02821},
Archiveprefix = {arXiv},
Arxivid = {1603.02821},
Author = {Rao, Sumathi},
Date-Added = {2018-12-19 17:21:12 +0530},
Date-Modified = {2018-12-19 17:21:14 +0530},
Eprint = {1603.02821},
File = {:Users/deepak/ownCloud/root/research/mendeley/Rao{\_}Weyl semi-metals A short review{\_}2016.html:html;:Users/deepak/ownCloud/root/research/mendeley/Rao{\_}Weyl semi-metals A short review{\_}2016.pdf:pdf},
Issn = {09704140},
Journal = {Journal of the Indian Institute of Science},
Keywords = {Condensed Matter - Mesoscale and Nanoscale Physics},
Month = {mar},
Number = {2},
Pages = {145--156},
Shorttitle = {Weyl semi-metals},
Title = {{Weyl semi-metals: A short review}},
Url = {http://arxiv.org/abs/1603.02821},
Volume = {96},
Year = {2016},
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Bdsk-Url-1 = {http://arxiv.org/abs/1603.02821}}
```