Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole

Carlip, Steven

doi:10.1088/0264-9381/22/12/r01

Cited by 306 publications

(370 citation statements)

References 238 publications

(502 reference statements)

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“…If this derivation of time slice metric in AdS 3 really explains the mechanism of emergence of AdS in AdS/CFT, it should fit nicely with the dynamics of AdS gravity for the whole 3D space-time. One natural coordinate system in 3D gravity for our argument is as follows It is also useful to remember that connections between Liouville theory and 3D AdS gravity were discussed in earlier papers [59][60][61][62][63][64][65][66] (refer to [67] for a review). Especially the direct connection between the equation of motion in the SL(2, R) Chern-Simons gauge theory description of AdS gravity [68] and that of Liouville theory was found in [61] (see also closely related arguments [62][63][64][65]).…”

Section: Liouville Equation and 3d Ads Gravitymentioning

confidence: 99%

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Caputa

Kundu

Miyaji

et al. 2017

J. High Energ. Phys.

285

402

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Abstract:We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

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Section: Liouville Equation and 3d Ads Gravitymentioning

confidence: 99%

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Caputa

Kundu

Miyaji

et al. 2017

J. High Energ. Phys.

285

402

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“…It is easy to show that by using thermodynamic quantities such as electric charge (3.14), entropy (3.15) and mass (3.16), with the first law of black hole thermodynamics 18) one can define the intensive parameters conjugate to S and Q. These quantities are the temperature and the electric potential 19) JHEP05 (2016)029 which are the same as those calculated for temperature (3.13) and electric potential (3.17). In other word, although massive term modifies some of thermodynamic quantities, the first law of thermodynamics is still valid.…”

Section: Thermodynamicsmentioning

confidence: 99%

“…Among them one can point out: providing simplified machinery for studying different properties of black holes such as thermodynamical ones [4][5][6][7][8][9][10], contributing to our understanding of gravitational systems and their interactions in lower dimensions [11], existence of specific relations between BTZ black holes and effective action in string theory [12][13][14][15] and possible existence of gravitational Aharonov-Bohm effect due to the noncommutative BTZ black holes [16]. In addition, several studies were conducted in context of AdS/CFT correspondence [17][18][19], quantum aspect of three dimensional gravity, entanglement, quantum entropy [20][21][22][23][24][25][26] and holographic aspects of such solutions [27][28][29]. Furthermore, three dimensional black holes and their thermodynamical properties in the presence of different matter fields with various gravity models are addressed in literature [30][31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Hendi

Panah

Panahiyan

2016

J. High Energ. Phys.

106

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Motivated by recent developments of BTZ black holes and interesting results of massive gravity, we investigate massive BTZ black holes in the presence of Maxwell and Born-Infeld (BI) electrodynamics. We study geometrical properties such as type of singularity and asymptotical behavior as well as thermodynamic structure of the solutions through canonical ensemble. We show that despite the existence of massive term, obtained solutions are asymptotically (a)dS and have a curvature singularity at the origin. Then, we regard varying cosmological constant and examine the Van der Waals like behavior of the solutions in extended phase space. In addition, we employ geometrical thermodynamic approaches and show that using Weinhold, Ruppeiner and Quevedo metrics leads to existence of ensemble dependency while HPEM metric yields consistent picture. For neutral solutions, it will be shown that generalization to massive gravity leads to the presence of non-zero temperature and heat capacity for vanishing horizon radius. Such behavior is not observed for linearly charged solutions while generalization to nonlinearly one recovers this property.

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“…The exact form of the 2D CFT dual to 3D AdS gravity still remains a controversial point [55][56][57]. However, in the large N regime (central charge c 1), i.e.…”

Section: Ads 3 Gravity and Dual Cftmentioning

confidence: 99%

Entanglement Entropy of AdS Black Holes

Cadoni

Melis

2010

Entropy

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We review recent progress in understanding the entanglement entropy of gravitational configurations for anti-de Sitter gravity in two and three spacetime dimensions using the AdS/CFT correspondence. We derive simple expressions for the entanglement entropy of two-and three-dimensional black holes. In both cases, the leading term of the entanglement entropy in the large black hole mass expansion reproduces exactly the Bekenstein-Hawking entropy, whereas the subleading term behaves logarithmically. In particular, for the BTZ black hole the leading term of the entanglement entropy can be obtained from the large temperature expansion of the partition function of a broad class of 2D CFTs on the torus.

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Conformal field theory, (2 + 1)-dimensional gravity and the BTZ black hole

Cited by 306 publications

References 238 publications

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Liouville action as path-integral complexity: from continuous tensor networks to AdS/CFT

Massive charged BTZ black holes in asymptotically (a)dS spacetimes

Entanglement Entropy of AdS Black Holes

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