Thermodynamics and Statistical Mechanics of Induced Liouville Gravity

Abstract

In this paper we describe a Liouville gravity which is induced by a set of quantum fields (constituents) and represents a two-dimensional analog of Sakharov's induced gravity. The important feature of the considered theory is the presence of massless constituents which are responsible for the appearance of the induced Liouville field. The role of the massive constituents is only to induce the cosmological constant. We consider the instanton solutions of the Euclidean Liouville gravity with negative and zero cosmological constants, some instantons being interpreted as two-dimensional anti-de Sitter $Ad{S}_2$ black holes. We study thermodynamics of all the solutions and conclude that their entropy is completely determined by the statistical-mechanical entropy of the massless constituents. This shows, in particular, that the constituents of the induced gravity are the true degrees of freedom of $Ad{S}_2$ black holes. Special attention is also paid to the induced Liouville gravity with zero cosmological constant on a torus. We demonstrate the equivalence of its thermodynamics to the thermodynamics of BTZ black holes and comment on computations of the BTZ black hole entropy.

arXiv comment22 pages, latex, no figures

References in corpus (25)

• The Black Hole in Three Dimensional Space Time
• Microscopic Origin of the Bekenstein-Hawking Entropy
• Geometric and Renormalized Entropy in Conformal Field Theory
• Black Hole Entropy from Near-Horizon Microstates
• Rotation and the AdS/CFT correspondence
• Black Hole Entropy from Conformal Field Theory in Any Dimension
• The asymptotic dynamics of three-dimensional Einstein gravity with a negative cosmological constant
• AdS2 Quantum Gravity and String Theory
• The Statistical Mechanics of the (2+1)-Dimensional Black Hole
• Exact Dirac Quantization of All 2-D Dilaton Gravity Theories
• What We Don't Know about BTZ Black Hole Entropy
• Thermal Fields, Entropy, and Black Holes
• Observables for Two-Dimensional Black Holes
• Mechanism of Generation of Black Hole Entropy in Sakharov's Induced Gravity
• Boundary dynamics and the statistical mechanics of the 2+1 dimensional black hole
• Statistical Origin of Black Hole Entropy in Induced Gravity
• The Bekenstein Formula and String Theory (N-brane Theory)
• On One-loop Quantum Corrections to the Thermodynamics of Charged Black Holes
• Black hole entropy: statistical mechanics agrees thermodynamics
• Black Hole Entropy: Off-Shell vs On-Shell
• Conformal Field Theory, Geometry, and Entropy
• A note on covariant action integrals in three dimensions
• Embeddings of the Virasoro algebra and black hole entropy
• Black Hole Entropy in Induced Gravity: Reduction to 2D Quantum Field Theory on the Horizon
• A Note on Entanglement Entropy and Conformal Field Theory

Cited by in corpus (19)

• Entanglement entropy of black holes
• Dilaton Gravity in Two Dimensions
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Vacuum States for AdS_2 Black Holes
• Black hole entropy without brick walls
• CFT and Black Hole Entropy in Induced Gravity
• Quantum-Corrected Cardy Entropy for Generic 1+1-Dimensional Gravity
• Emergent Gravity as the Eraser of Anomalous Gauge Boson Masses, and QFT-GR Concord
• Liouville Lost, Liouville Regained: Central Charge in a Dynamical Background
• Indication for unsmooth horizon induced by quantum gravity interaction
• Horizon State, Hawking Radiation and Boundary Liouville Model
• 2D Black Holes, Conformal Vacua and CFTs on the Cylinder
• Twisted sectors in three-dimensional gravity
• Reduction of BTZ spacetime to hypersurfaces of foliation
• Statistical Mechanics of Charged Black Holes in Induced Einstein-Maxwell Gravity
• The AdS/CFT correspondence in two dimensions
• Ensemble averages, Poisson processes and Microstates
• Thermodynamics of nonspherical black holes from Liouville theory
• Holographic Central Charge for 2-Dimensional de Sitter Space