CFT/Gravity Correspondence on the Isolated Horizon

TL;DR

This paper establishes a precise CFT/gravity correspondence at isolated horizons, showing how conformal symmetry and Kac-Moody algebras encode horizon degrees of freedom, reproducing Bekenstein-Hawking entropy without large corrections.

Contribution

It introduces a novel CFT/gravity correspondence framework on isolated horizons using Kac-Moody algebras and boundary conditions, linking horizon states to conformal field theory.

Findings

Derivation of a local conformal symmetry at each horizon puncture.

Representation of gravitational fluxes via Kac-Moody zero modes.

Reproduction of Bekenstein-Hawking entropy without large quantum corrections.

Abstract

A quantum isolated horizon can be modeled by an SU(2) Chern-Simons theory on a punctured 2-sphere. We show how a local 2-dimensional conformal symmetry arises at each puncture inducing an infinite set of new observables localized at the horizon which satisfy a Kac-Moody algebra. By means of the isolated horizon boundary conditions, we represent the gravitational fluxes degrees of freedom in terms of the zero modes of the Kac-Moody algebra defined on the boundary of a punctured disk. In this way, our construction encodes a precise notion of CFT/gravity correspondence. The higher modes in the algebra represent new nongeometric charges which can be represented in terms of free matter field degrees of freedom. When computing the CFT partition function of the system, these new states induce an extra degeneracy factor, representing the density of horizon states at a given energy level, which reproduces the Bekenstein's holographic bound for an imaginary Immirzi parameter. This allows us to recover the Bekenstein-Hawking entropy formula without the large quantum gravity corrections associated with the number of punctures.