CFT and Black Hole Entropy in Induced Gravity

TL;DR

This work shows that black hole entropy in induced gravity arises from a near-horizon conformal structure by dimensional reduction: the 4D theory decomposes into a spectrum of 2D induced gravities labeled by horizon momentum $p$, each described by a CFT with a central charge determined by spin and non-minimal couplings and with a correlation length set by masses and $p$. By computing a partial entropy $s(p)$ from the 2D CFT data and integrating over all transverse momenta, the authors recover the Bekenstein-Hawking entropy $S^{BH}= ext{Area}/(4G)$, thus providing a concrete microscopic realization of Carlip's near-horizon CFT approach within a controllable model. The analysis clarifies how masses and non-minimal couplings break conformal invariance and how positive total entropy emerges despite possible negative central charges, offering a framework to study RG-like behavior and the role of horizon-induced entanglement in black hole thermodynamics.

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.