Research

“Loop Quantum Gravity is Dead … ”

… is a phrase that many high energy theorists, especially those of the stringy persuasion, long to hear. Fortunately, to borrow a phrase from Mark Twain, reports of the death of loop quantum gravity (LQG) are greatly exaggerated.

Premature declarations of the imminent demise of LQG have a long history. The most recent one comes from a recent article in Quanta magazine:

Santos noted that “the only theory out there” that unifies the fundamental forces in a single framework is string theory. Rival approaches such as loop quantum gravity attempt to quantize gravity by dividing space-time into pieces, without connecting gravity with the other forces. “If the weak gravity conjecture is correct, things like loop quantum gravity are dead,” said Santos. [emph mine]

Santos follows in the footsteps of a long line of illustrious predecessors who have, at various points and for various reasons, declared LQG either dead or dying. I list a few of these here.

Lubos Motl on his blog post on the weak gravity conjecture states:

… pure theories of quantum gravity cannot work. This conclusion … applies to various loop quantum gravities, spin foams, causal and acausal, dynamical and non-dynamical triangulations, tetrahedronizations, and any other misinterpretations of quantum gravity that you have heard of.

‘t Hooft in [1] says:

… there [has] been an abundance of completely wild concoctions [for theories of quantum gravity] that serious researchers have come up with. Lack of phantasy is not our problem [9][10][11]

where the papers he cites as examples of “wild concoctions” include Sorkin’s causal set theory [2], Rovelli’s 1997 review of LQG [3] and an review of causal dynamical triangulations (CDT) [4].

To be fair to ‘t Hooft, in the same paper he also expresses his long standing skepticism about string theory:

… String theory was an interesting guess, but may well have been a too wild one.

Of course, there have been no dearth of similar declarations for string theory also. The most famous one was likely said by Stephen Hawking in 1979. Referring to the fact that $N=8$ supergravity (1) in 10 dimensions was a unitary and renormalizable theory Hawking apparently stated at a conference something along the lines of “Physics is over”. He said as much in a Physics Today article in 1981 [5] titled “Is the End in Sight for Theoretical Physics?” Of course, the implied conclusion is that String Theory, which was yet to cured of its troublesome anomalies in the so-called first superstring revolution of 1985, was also a dead, or even worse, an irrelevant theory.

More recently there has been there has been critical tome titled “Note Even Wrong” by Peter Woit [6]. The title is chosen for devastating effect to suggest that string theory, far from being right, is “not even wrong” in that it provides no falsifiable predictions which might be observable in any near or medium term (10-50 years) experiments. Of course, the lack of falsifiable predictions does not prove that none of the physical insights gained from string theory, such as the various dualities relating large and small scales and relating theories with large and small couplings, are going to be found to be relevant for whatever form a correct, consistent theory of quantum gravity might take in the future. On the contrary, any final theory of quantum gravity will contain many of the ingredients discovered by string theorists such as the existence of non-perturbative extended objects such as one dimensional strings and higher dimensional branes.

The most important of these ingredients is the statement of holography(2) – that physics of a gravity theory in a $D+1$ dimensional anti de-Sitter (AdS) spacetime can be mapped to the physics of a $D$ dimensional conformal field theory living on the boundary of that spacetime.

The important lesson is that string theory has gone through a great many ups and downs during its long history. In fact, the situation has now reached a stage that what used to be known as the “string landscape” is now referred to as the “string swampland” and there is an entire industry of research into “swampland” physics built around this concept. I wonder how many further stages of devolution will have to occur, from landscape to swampland to festering pits of doom, before string theorists try to adopt a more pragmatic and less dogmatic approach to quantum gravity research. The irony of the situation can be seen in this video of a “Vision discussion” held at the end of the most recent Strings conference. Near the beginning of this discussion Daniel Harlow feels the need to state that “I think string theory is still a good candidate for quantum gravity”! During the rest of the discussion one would be hard pressed to find any actual references to string theory!

Similarly, it is highly premature to declare LQG to be “dead” based on the possibility that the weak gravity conjecture might be correct. The physical insights which have been gained from LQG research, such as the quantization of geometric operators and the construction of a spin network basis for the Hilbert space of quantum geometry, are very much likely to be part of the ultimate quantum gravity theory. In fact, a lot of what passes as “string theory” research these days is actually work done in the context of so-called “tensor networks” applied to the AdS-CFT correspondence. And, unsurprisingly enough for those not inclined towards partisan politics such as myself, tensor networks are nothing more than the spin networks of LQG!(3)

Of course, string theorists would be loath to admit the bitter fact that one of their primary successes, and one which comes closest to providing some sort of falsifiable predictions, ends up relying on precisely the same elementary building blocks discovered more than 30 years ago by theorists working on something known as loop quantum gravity!

The weak gravity conjecture may very well be correct. There have been several recent claimed proofs in the literature [7, 8, 9]. However, all of these are based on arguments involving quantum field theory and string theory. What makes the most persuasive argument in favour of the WGC, in my humble opinion, is a paper by Shahar Hod [10]. He shows, using arguments based on the relaxation times of the quasinormal modes of near-extremal Reissner-Nordstrom black holes, that the WGC must hold if a certain other conjecture (also framed and proved for several particular cases by Hod) regarding the “universal relaxation bound” for a thermodynamic system is true. This argument does not require any knowledge of the UV field theory and makes no assumptions about the nature of the quantum gravity theory. These facts are what make Hod’s proof particularly compelling in my view.

Given the preponderance of evidence in favour of the WGC, is it correct to conclude that LQG is “dead”? The answer to that is a resounding “no”. On the contrary, this fact now throws up a challenge to the LQG community, who have thus far ignored the physics of charged extremal black holes for the most part, to explore that region of the theory space and to inquire what new insights the correctness of the WGC implies for the structure of LQG. The path towards this understanding, in my opinion, lies in understanding how to model the quantum geometry of charged AdS black holes along the lines discussed in one of my previous blog posts.

• (1) Where $N$ refers to the number of supersymmetric charges in the theory.
• (2) also known as the AdS-CFT correspondence or the Maldacena conjecture.
• (3) At this point one might ask how is this the case, to which I would reply “spin networks and tensor networks are the same thing in the same way as a red ball and a blue ball are both balls”! Further details to appear in a not too distant blog post or arXiv paper.

[1] G. t-Hooft, “Nature’s book keeping system,” Arxiv preprint arxiv:1605.00027, 2016.
[Bibtex]
@article{t-Hooft2016Natures,
Annote = {Wherein t'Hooft basically refers to LQG and associated
work as "completely wild concoctions" and "phantasy". When
such senior theorists dismiss LQG in this way, is it any
surprise that there exists a huge social gap between the
LQG and String communities?},
Author = {t-Hooft, Gerard},
Date-Modified = {2016-05-17 23:57:59 +0530},
Journal = {arXiv preprint arXiv:1605.00027},
Title = {Nature's Book Keeping System},
Year = {2016},
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[2] R. D. Sorkin, “Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School),” Arxiv:gr-qc/0309009, 2003.
[Bibtex]
@article{Sorkin2003Causal,
Abstract = {These are lecture notes on causal set theory prepared in Jan. 2002 for a Summer School in Valdivia, Chile. In some places, they are more complete, in others much less so, regrettably. An extensive set of references and a glossary of terms can be found at the end of the notes.},
Archiveprefix = {arXiv},
Arxivid = {gr-qc/0309009},
Author = {Sorkin, Rafael D.},
Date-Modified = {2018-12-31 23:31:31 +0530},
Doi = {10.1007/0-387-24992-3_7},
Eprint = {0309009},
File = {:Users/deepak/ownCloud/root/research/mendeley/Sorkin{\_}Causal Sets Discrete Gravity (Notes for the Valdivia Summer School){\_}2003.pdf:pdf},
Isbn = {0-387-23995-2},
Issn = {{\textless}null{\textgreater}},
Journal = {arXiv:gr-qc/0309009},
Keywords = {Astrophysics,General Relativity and Quantum Cosmology,High Energy Physics - Theory},
Mendeley-Groups = {Zotero - Unifying Strings and Loops,Zotero - Zotero Library},
Mendeley-Tags = {Astrophysics,General Relativity and Quantum Cosmology,High Energy Physics - Theory},
Month = {sep},
Primaryclass = {gr-qc},
Shorttitle = {Causal Sets},
Title = {{Causal Sets: Discrete Gravity (Notes for the Valdivia Summer School)}},
Url = {http://arxiv.org/abs/gr-qc/0309009},
Year = {2003},
Bdsk-Url-1 = {http://arxiv.org/abs/gr-qc/0309009},
Bdsk-Url-2 = {https://doi.org/10.1007/0-387-24992-3_7}}
[3] C. Rovelli, Loop Quantum Gravity, 1997.
[Bibtex]
@misc{Rovelli1997Loop,
Abstract = {The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. The research in loop quantum gravity forms today a vast area, ranging from mathematical foundations to physical applications. Among the most significative results obtained are: (i) The computation of the physical spectra of geometrical quantities such as area and volume; which yields quantitative predictions on Planck-scale physics. (ii) A derivation of the Bekenstein-Hawking black hole entropy formula. (iii) An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime foam''. Long standing open problems within the approach (lack of a scalar product, overcompleteness of the loop basis, implementation of reality conditions) have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.},
Author = {Carlo Rovelli},
Comments = {Review paper written for the electronic journal Living Reviews'. 34 pages},
Date-Modified = {2019-01-01 00:15:31 +0530},
Doi = {10.12942/lrr-1998-1},
Eprint = {arXiv:gr-qc/9710008},
Howpublished = {LivingRev.Rel.1:1,1998},
Title = {{L}oop {Q}uantum {G}ravity},
Url = {http://arxiv.org/abs/gr-qc/9710008},
Year = {1997},
Bdsk-Url-1 = {http://arxiv.org/abs/gr-qc/9710008},
Bdsk-Url-2 = {https://doi.org/10.12942/lrr-1998-1}}
[4] J. Ambjorn, A. Goerlich, J. Jurkiewicz, and R. Loll, Quantum gravity via causal dynamical triangulations, 2013.
[Bibtex]
@misc{Ambjorn2013Quantum,
Abstract = {"Causal Dynamical Triangulations" ({CDT}) represent a
lattice regularization of the sum over spacetime histories,
providing us with a non-perturbative formulation of quantum
gravity. The ultraviolet fixed points of the lattice theory
can be used to define a continuum quantum field theory,
potentially making contact with quantum gravity defined via
asymptotic safety. We describe the formalism of {CDT}, its
phase diagram, and the quantum geometries emerging from it.
We also argue that the formalism should be able to describe
a more general class of quantum-gravitational models of
{Horava-Lifshitz} type.},
Archiveprefix = {arXiv},
Author = {Ambjorn, J. and Goerlich, A. and Jurkiewicz, J. and Loll, R.},
Citeulike-Article-Id = {12015297},
Date-Modified = {2013-12-05 18:47:23 +0530},
Day = {8},
Eprint = {1302.2173},
Keywords = {asymptotic\_safety, b\_dittrich, causal\_dynamical\_triangulations, fixed\_point, gorlich\_a, horava\_lifshitz, jurkiewicz\_j, lattice\_models, manybody, non-perturbative, phase\_transition, quantum\_gravity, renate\_loll},
Month = feb,
Posted-At = {2013-12-05 13:11:27},
Priority = {2},
Title = {Quantum Gravity via Causal Dynamical Triangulations},
Url = {http://arxiv.org/abs/1302.2173},
Year = {2013},
Bdsk-Url-1 = {http://arxiv.org/abs/1302.2173}}
[5] S. W. Hawking, “Is the End in Sight for Theoretical Physics?,” Physics bulletin, vol. 32, iss. 1, p. 15, 1981.
[Bibtex]
@article{Hawking1981Is-the-End-in-Sight,
Author = {Hawking, S W},
Date-Modified = {2020-06-22 23:54:20 +0530},
Doi = {10.1088/0031-9112/32/1/024},
File = {:Users/deepak/ownCloud/root/research/mendeley/Hawking{\_}Is the End in Sight for Theoretical Physics{\_}1981.pdf:pdf},
Issn = {0031-9112},
Journal = {Physics Bulletin},
Mendeley-Groups = {History},
Number = {1},
Pages = {15},
Publisher = {IOP Publishing},
Title = {{Is the End in Sight for Theoretical Physics?}},
Volume = {32},
Year = {1981},
Bdsk-Url-1 = {https://doi.org/10.1088/0031-9112/32/1/024}}
[6] P. Woit, Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law, , 2006.
[Bibtex]
@book{Woit2006Not-Even,
Abstract = {'Not Even Wrong' describes the attempts of human beings to understand how the world works at the most fundamental level and what the role of mathematics is in its description. The author's perspective is unusual in that he is sceptical about string theory, which has dominated his field for 20 years.},
Author = {Woit, Peter},
Date-Modified = {2020-06-23 00:02:17 +0530},
Isbn = {0465092756},
Mendeley-Groups = {String Theory,History},
Pages = {320},
Title = {{Not Even Wrong: The Failure of String Theory and the Search for Unity in Physical Law}},
Url = {https://www.amazon.com/Not-Even-Wrong-Failure-Physical/dp/0465092764 http://www.amazon.com/dp/0465092756},
Year = {2006},
Bdsk-Url-1 = {https://www.amazon.com/Not-Even-Wrong-Failure-Physical/dp/0465092764%20http://www.amazon.com/dp/0465092756}}
[7] C. Cheung and G. N. Remmen, “Naturalness and the weak gravity conjecture,” Physical review letters, vol. 113, iss. 5, 2014.
[Bibtex]
@article{Cheung2014Naturalness,
Abstract = {The weak gravity conjecture (WGC) is an ultraviolet consistency condition asserting that an Abelian force requires a state of charge q and mass m with q{\textgreater}m/mPl. We generalize the WGC to product gauge groups and study its tension with the naturalness principle for a charged scalar coupled to gravity. Reconciling naturalness with the WGC either requires a Higgs phase or a low cutoff at IqmPl. If neither applies, one can construct simple models that forbid a natural electroweak scale and whose observation would rule out the naturalness principle. {\textcopyright} 2014 American Physical Society.},
Archiveprefix = {arXiv},
Arxivid = {1402.2287},
Author = {Cheung, Clifford and Remmen, Grant N.},
Date-Modified = {2020-06-23 00:38:04 +0530},
Doi = {10.1103/PhysRevLett.113.051601},
Eprint = {1402.2287},
File = {:Users/deepak/ownCloud/root/research/mendeley/Cheung, Remmen{\_}Naturalness and the Weak Gravity Conjecture{\_}2014.pdf:pdf},
Issn = {10797114},
Journal = {Physical Review Letters},
Mendeley-Groups = {Black Hole Evaporation,Quantum Gravity},
Number = {5},
Title = {{Naturalness and the weak gravity conjecture}},
Url = {http://arxiv.org/abs/1402.2287 http://dx.doi.org/10.1103/PhysRevLett.113.051601 https://arxiv.org/abs/1402.2287},
Volume = {113},
Year = {2014},
Bdsk-Url-1 = {http://arxiv.org/abs/1402.2287%20http://dx.doi.org/10.1103/PhysRevLett.113.051601%20https://arxiv.org/abs/1402.2287},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.113.051601}}
[8] C. Cheung, J. Liu, and G. N. Remmen, “Proof of the weak gravity conjecture from black hole entropy,” Journal of high energy physics, vol. 2018, iss. 10, 2018.
[Bibtex]
@article{Cheung2018Proof,
Abstract = {We prove that higher-dimension operators contribute positively to the entropy of a thermodynamically stable black hole at fixed mass and charge. Our results apply whenever the dominant corrections originate at tree level from quantum field theoretic dynamics. More generally, positivity of the entropy shift is equivalent to a certain inequality relating the free energies of black holes. These entropy inequalities mandate new positivity bounds on the coefficients of higher-dimension operators. One of these conditions implies that the charge-to-mass ratio of an extremal black hole asymptotes to unity from above for increasing mass. Consequently, large extremal black holes are unstable to decay to smaller extremal black holes and the weak gravity conjecture is automatically satisfied. Our findings generalize to arbitrary spacetime dimension and to the case of multiple gauge fields. The assumptions of this proof are valid across a range of scenarios, including string theory constructions with a dilaton stabilized below the string scale.},
Archiveprefix = {arXiv},
Arxivid = {1801.08546},
Author = {Cheung, Clifford and Liu, Junyu and Remmen, Grant N.},
Date-Modified = {2020-06-23 00:38:04 +0530},
Doi = {10.1007/JHEP10(2018)004},
Eprint = {1801.08546},
File = {:Users/deepak/ownCloud/root/research/mendeley/Cheung, Liu, Remmen{\_}Proof of the weak gravity conjecture from black hole entropy{\_}2018.pdf:pdf},
Issn = {10298479},
Journal = {Journal of High Energy Physics},
Keywords = {Black Holes,Effective Field Theories},
Number = {10},
Title = {{Proof of the weak gravity conjecture from black hole entropy}},
Url = {http://arxiv.org/abs/1801.08546 http://dx.doi.org/10.1007/JHEP10(2018)004 https://arxiv.org/abs/1801.08546},
Volume = {2018},
Year = {2018},
Bdsk-Url-1 = {http://arxiv.org/abs/1801.08546%20http://dx.doi.org/10.1007/JHEP10(2018)004%20https://arxiv.org/abs/1801.08546},
Bdsk-Url-2 = {https://doi.org/10.1007/JHEP10(2018)004}}
[9] Y. Hamada, T. Noumi, and G. Shiu, “Weak Gravity Conjecture from Unitarity and Causality,” Physical review letters, vol. 123, iss. 5, 2019.
[Bibtex]
@article{Hamada2019Weak,
Abstract = {The weak gravity conjecture states that quantum gravity theories have to contain a charged state with a charge-to-mass ratio bigger than unity. By studying unitarity and causality constraints on higher derivative corrections to the charge-to-mass ratio of extremal back holes, we demonstrate that heavy extremal black holes can play the role of the required charged state under several assumptions. In particular, our argument is applicable when the higher-spin states Reggeizing graviton exchange are subdominant in the photon scattering. It covers (1) theories with light neutral bosons such as dilaton and moduli, and (2) UV completion where the photon and the graviton are accompanied by different sets of Regge states just like open string theory. Our result provides an existence proof of the weak gravity conjecture in a wide class of theories, including generic string theory setups with the dilaton or other moduli stabilized below the string scale.},
Archiveprefix = {arXiv},
Arxivid = {1810.03637},
Author = {Hamada, Yuta and Noumi, Toshifumi and Shiu, Gary},
Date-Modified = {2020-05-19 10:12:32 +0530},
Doi = {10.1103/PhysRevLett.123.051601},
Eprint = {1810.03637},
File = {:Users/deepak/ownCloud/root/research/mendeley/Hamada, Noumi, Shiu{\_}Weak Gravity Conjecture from Unitarity and Causality{\_}2018.pdf:pdf},
Issn = {10797114},
Journal = {Physical Review Letters},
Number = {5},
Title = {{Weak Gravity Conjecture from Unitarity and Causality}},
Url = {http://arxiv.org/abs/1810.03637 http://dx.doi.org/10.1103/PhysRevLett.123.051601 https://arxiv.org/abs/1810.03637},
Volume = {123},
Year = {2019},
Bdsk-Url-1 = {http://arxiv.org/abs/1810.03637%20http://dx.doi.org/10.1103/PhysRevLett.123.051601%20https://arxiv.org/abs/1810.03637},
Bdsk-Url-2 = {https://doi.org/10.1103/PhysRevLett.123.051601}}
[10] S. Hod, “A proof of the weak gravity conjecture,” International journal of modern physics d, p. 1742004, 2017.
[Bibtex]
@article{Hod2017A-proof,
Author = {Hod, Shahar},
Bdsk-Url-1 = {https://arxiv.org/abs/1705.06287}}`