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

TL;DR

This paper demonstrates how to restore the central charge in Liouville theory coupled to a dynamical background by imposing specific boundary conditions, crucial for understanding black hole entropy.

Contribution

It introduces a method to recover the classical central charge in dynamical backgrounds by applying suitable boundary constraints.

Findings

Central charge vanishes without boundary conditions in dynamical backgrounds.

Appropriate fall-off conditions restore the central charge.

Implications for black hole entropy calculations.

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.