Quantum Hall Effect and Black Hole Entropy in Loop Quantum Gravity

Question

Referee this paper: [arXiv:1208.3335]

Please use comments to point to previous work in this direction, and reviews to referee the accuracy of the paper. Feel free to edit this submission to summarise the paper (just click on edit, your summary will then appear under the horizontal line)

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(ArXiV abstract)

In LQG, black hole horizons are described by 2+1 dimensional boundaries of a bulk 3+1 dimensional spacetime. The horizon is endowed with area by lines of gravitational flux which pierce the surface. As is well known, counting of the possible states associated with a given set of punctures allows us to recover the famous Bekenstein-Hawking area law according to which the entropy of a black hole is proportional to the area of the associated horizon $ S_{BH} \propto A_{Hor} $. It is also known that the dynamics of the horizon degrees of freedom is described by the Chern-Simons action of a $\mathfrak{su(2)}$ (or $\mathfrak{u(1)}$ after a certain gauge fixing) valued gauge field $A_{\mu}^i$. Recent numerical work which performs the state-counting for punctures, from first-principles, reveals a step-like structure in the entropy-area relation. We argue that both the presence of the Chern-Simons action and the step-like structure in the entropy-area curve are indicative of the fact that the effective theory which describes the dynamics of punctures on the horizon is that of the Quantum Hall Effect.

Comments

@DeepakVaid It appears that you have cited Entropy of Non-extremal black holes from loop gravity, so you may be interested in Lubos's review of the citation here (originally on his blog). Please don't be offended by the first line of his post : )

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Thanks for that link, @dimension10. Unfortunately, Lubos' is afflicted with some sort of LQG-phobia, so I can't really take anything he says on the topic seriously. His "review" is little more than a collection of snide remarks. Its a loss for physics, actually. Someone with his intellect could contribute so much towards bringing string and lqg into a unified framework, if only he could drop his irrational fears of LQG and actually study the subject! BTW plz feel free to ask any - no matter how seemingly trivial - questions about my work.

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Phil Gibbs is somewhat interested in the unification of strings and LQG ...

Maybe he would be willing to look at your work in detail and write a review, if you ask him (on his blog for example)? He is also on PhysicsOverflow but I am not sure how often he looks on the site.