Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity

Carlip, Steven

doi:10.1088/0264-9381/22/14/014

Cited by 63 publications

(86 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

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

View full text Add to dashboard Cite

show abstract

“…thed variables, we obtain an action that is much more transparent. This is particularly relevant if one wants to understand ther variables as degrees of freedom which describe the position of the boundary in the embedding spacetime, as in a proposal of Carlip in [33,34] for the AdS case.…”

Section: Jhep03(2016)208mentioning

confidence: 99%

3D holography: from discretum to continuum

Bonzom

Dittrich

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

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.

show abstract

“…This can be done in three spacetime dimensions [41]; whether this approach can be extended to higher dimensions is uncertain. • It ought to be possible to couple boundary degrees of freedom to matter and connect the results to Hawking radiation.…”

Section: What Are the States?mentioning

confidence: 99%

Effective conformal descriptions of black hole entropy: A review

Carlip

2012

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. Black holes behave as thermodynamic objects, and it is natural to ask for an underlying "statistical mechanical" explanation in terms of microscopic degrees of freedom. I summarize attempts to describe these degrees of freedom in terms of a dual two-dimensional conformal field theory, emphasizing the generality of the Cardy formula and the consequent universal nature of the conformal description.

show abstract

Dynamics of asymptotic diffeomorphisms in (2+1)-dimensional gravity

Cited by 63 publications

References 34 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

3D holography: from discretum to continuum

Effective conformal descriptions of black hole entropy: A review

Contact Info

Product

Resources

About