Liouville Lost, Liouville Regained: Central Charge in a Dynamical Background

Abstract

Several recent approaches to black hole entropy obtain the density of states from the central charge of a Liouville theory. If Liouville theory is coupled to a dynamical spacetime background, however, the classical central charge vanishes. I show that the central charge can be restored by introducing appropriate constraints, which may be interpreted as fall-off conditions at a boundary such as a black hole horizon.

8 pages, LaTeX, no figures; reference added

References in corpus (5)

• Entropy from Conformal Field Theory at Killing Horizons
• Quantum effective action from the AdS/CFT correspondence
• Black Hole Entropy from Horizon Conformal Field Theory
• Holonomies, anomalies and the Fefferman-Graham ambiguity in AdS3 gravity
• The Fefferman-Graham Ambiguity and AdS Black Holes

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• Horizon conformal entropy in Gauss-Bonnet gravity
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• Quantum-Corrected Cardy Entropy for Generic 1+1-Dimensional Gravity
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• Testing Holographic Principle from Logarithmic and Higher Order Corrections to Black Hole Entropy
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• Can One Understand Black Hole Entropy without Knowing Much about Quantum Gravity?
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