Liouville Theory on Horizons: Towards a Quantum Theory of Black Holes

Abstract

We show that any nonextremal black hole can be described by a Liouville theory that lives on its very near horizon region. In classical Liouville theory, the black hole corresponds to a field configuration that reproduces the Rindler metric. In quantum Liouville theory, the black hole state in the CFT is created by the puncture operator that gives rise to a conical singularity with a deficit angle of $2\pi$. This state is "heavy" with a nonnormalizable wave function in the minisuperspace approximation. Black hole entropy counts the number of ways the "heavy" black hole state can be obtained by acting with a product of "light, quantum" operators in the CFT. Black hole hair is described by the "background charge" in the CFT but its physical nature is unclear.

31 pages

References in corpus (9)

• Noether current from the surface term of gravitational action, Virasoro algebra and horizon entropy
• Perturbative String Thermodynamics near Black Hole Horizons
• Black Holes as Conformal Field Theories on Horizons
• Dynamics of Diffeomorphism Degrees of Freedom at a Horizon
• Horizon Conformal Field Theories from $Ad{S}_2$ Black Holes
• Rindler Energy is Wald Entropy
• On the Holographic Nature Of Rindler Energy
• Extremal Black Hole Entropy from Horizon Conformal Field Theories
• Two Dimensional Conformal Symmetry and the Microscopic Interpretation of Black Hole Entropy

Cited by in corpus (7)

• The Holographic Entanglement Entropy of Schwarzschild Black Holes
• Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics
• Schwarzschild Black Holes and Asymptotic $Ad{S}_2$
• Black Hole Entropy and the Pseudo Goldstone Bosons of Conformal Symmetry
• Computing Black Hole Entropy at Infinity
• Wheeler-DeWitt equation in Null-foliated spacetimes
• Are Near $Ad{S}_2$ Spacetimes Dual to $Ad{S}_2$ Black Holes?