CFT and Black Hole Entropy in Induced Gravity

TL;DR

This paper derives black hole entropy in induced gravity models by reducing the 4D theory to 2D sectors near the horizon, showing that conformal field theory methods accurately reproduce the Bekenstein-Hawking entropy.

Contribution

It provides a novel derivation of black hole entropy using conformal properties of induced gravity constituents near the horizon, linking 2D CFT descriptions to 4D entropy.

Findings

Partial entropies $s(p)$ are computed using CFT methods for each 2D sector.

Sum of partial entropies reproduces the Bekenstein-Hawking entropy.

Supports the idea of a microscopic CFT-based explanation for black hole entropy.

Abstract

We present a derivation of the entropy of black holes in induced gravity models based on conformal properties of induced gravity constituents near the horizon. The four-dimensional (4D) theory is first reduced to a tower of two-dimensional (2D) gravities such that each 2D theory is induced by fields with certain momentum $p$ along the horizon. We demonstrate that in the vicinity of the horizon constituents of the 2D induced gravities are described by conformal field theories (CFT) with specific central charges depending on spin and non-minimal couplings and with specific correlation lengths depending on the masses of fields and on the momentum $p$. This enables one to use CFT methods to count partial entropies $s(p)$ in each 2D sector. The sum of partial entropies correctly reproduces the Bekenstein-Hawking entropy of the 4D induced gravity theory. Our results indicate that earlier attempts of the derivation of the entropy of black holes based on a near-horizon CFT may have a microscopic realization.