BTZ Black Hole Entropy and the Turaev–Viro Model

Geiller, Marc; Noui, Karim

doi:10.1007/s00023-014-0331-7

Cited by 7 publications

(10 citation statements)

References 77 publications

(144 reference statements)

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“…It is also worth mentioning that in the calculation of [7] (formula (16)) the entropy was dominated by small spins, whereas according to loop quantum gravity [6], it is the large spins which dominate the entropy. In the present paper we have agreed with the loop quantum gravity calculation at least in that direction since after considering the Wick rotation we have freed ourselves from the spin dependence of formula (16).…”

Section: Discussionsupporting

confidence: 81%

“…In [16] the method followed to compute the entropy of BTZ resembles ours and at the same time improves our result by proceeding with innovative ideas. The solid torus is triangulated with an even number of edges at the horizon.…”

Section: The Btz Black Hole Entropymentioning

confidence: 66%

“…A recursion formula is computed in order to show that the partition function of BTZ is completely determined by the partition function with an observable composed of only one edge. This very nice result of [16] changes everything afterwards since it is from this idea that the results of canonical and spin foam quantisation start to agree. The partition function with an observable composed of one edge is shown to reproduce the number of states which gives rise to the entropy in the canonical formulation.…”

Section: The Btz Black Hole Entropymentioning

confidence: 83%

“…However, we must point out that while dealing with corrections of the present work, a new paper has appeared [16], which deals with calculating the entropy using the Turaev-Viro model. Reference [16] exploits the idea of the observables, which were introduced in [17] and which have been used by the present author in dealing with the entropy of the BTZ black hole.…”

Section: The Btz Black Hole Entropymentioning

confidence: 99%

See 3 more Smart Citations

BTZ black hole entropy in loop quantum gravity and in spin foam models

García-Islas

2014

Gen Relativ Gravit

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Section: Discussionsupporting

confidence: 81%

Section: The Btz Black Hole Entropymentioning

confidence: 66%

Section: The Btz Black Hole Entropymentioning

confidence: 83%

Section: The Btz Black Hole Entropymentioning

confidence: 99%

See 2 more Smart Citations

BTZ black hole entropy in loop quantum gravity and in spin foam models

García-Islas

2014

Gen Relativ Gravit

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“…It has been suggested that the corresponding partition function can be obtained from the Turaev-Viro model, which describes 3D gravity with positive cosmological constant, by an analytical continuation [104]. Here we pointed out the importance of considering the continuum limit on the boundary, in particular if one wishes to obtain a description in terms of a dual field.…”

Section: Jhep03(2016)208mentioning

confidence: 99%

3D holography: from discretum to continuum

Bonzom

Dittrich

2016

J. High Energ. Phys.

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Abstract:We study the one-loop partition function of 3D gravity without cosmological constant on the solid torus with arbitrary metric fluctuations on the boundary. To this end we employ the discrete approach of (quantum) Regge calculus. In contrast with similar calculations performed directly in the continuum, we work with a boundary at finite distance from the torus axis. We show that after taking the continuum limit on the boundary -but still keeping finite distance from the torus axis -the one-loop correction is the same as the one recently found in the continuum in Barnich et al. for an asymptotically flat boundary. The discrete approach taken here allows to identify the boundary degrees of freedom which are responsible for the non-trivial structure of the one-loop correction. We therefore calculate also the Hamilton-Jacobi function to quadratic order in the boundary fluctuations both in the discrete set-up and directly in the continuum theory. We identify a dual boundary field theory with a Liouville type coupling to the boundary metric. The discrete set-up allows again to identify the dual field with degrees of freedom associated to radial bulk edges attached to the boundary. Integrating out this dual field reproduces the (boundary diffeomorphism invariant part of the) quadratic order of the Hamilton-Jacobi functional. The considerations here show that bulk boundary dualities might also emerge at finite boundaries and moreover that discrete approaches are helpful in identifying such dualities.

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Quasi-local holographic dualities in non-perturbative 3d quantum gravity I – Convergence of multiple approaches and examples of Ponzano–Regge statistical duals

et al. 2019

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This is the first of a series of papers dedicated to the study of the partition function of three-dimensional quantum gravity on the twisted solid torus with the aim to deepen our understanding of holographic dualities from a non-perturbative quantum gravity perspective. Our aim is to compare the Ponzano-Regge model for non-perturbative three-dimensional quantum gravity with the previous perturbative calculations of this partition function. We begin by reviewing the results obtained in the past ten years via a wealth of different approaches, and then introduce the Ponzano-Regge model in a self-contained way. Thanks to the topological nature of three-dimensional quantum gravity we can solve exactly for the bulk degrees of freedom and identify dual boundary theories which depend on the choice of boundary states, that can also describe finite, non-asymptotic boundaries. This series of papers aims precisely at the investigation of the role played by the different quantum boundary conditions leading to different boundary theories. Here, we will describe the spin network boundary states for the Ponzano-Regge model on the twisted torus and derive the general expression for the corresponding partition functions. We identify a class of boundary states describing a tessellation with maximally fuzzy squares for which the partition function can be explicitly evaluated. In the limit case of a large, but finely discretized, boundary we find a dependence on the Dehn twist angle characteristic for the BMS 3 character. We furthermore show how certain choices of boundary states lead to known statistical models as dual field theories -but with a twist. * Electronic address: bdittrich@perimeterinstitute.ca † Electronic address: christophe.goeller@ens-lyon.fr ‡ Electronic address: etera.livine@ens-lyon.fr § Electronic address: ariello@perimeterinstitute.ca arXiv:1710.04202v1 [hep-th]

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BTZ Black Hole Entropy and the Turaev–Viro Model

Cited by 7 publications

References 77 publications

BTZ black hole entropy in loop quantum gravity and in spin foam models

BTZ black hole entropy in loop quantum gravity and in spin foam models

3D holography: from discretum to continuum

Quasi-local holographic dualities in non-perturbative 3d quantum gravity I – Convergence of multiple approaches and examples of Ponzano–Regge statistical duals

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