Entropy of the 3-brane and the AdS/CFT duality from a two-dimensional perspective

TL;DR

This paper uses a 2D scalar-tensor gravity model to analyze the entropy of near-extremal black 3-branes, revealing a power-law temperature dependence and illustrating how finite temperature effects in AdS/CFT can be captured by an AdS2/CFT1 duality with symmetry-breaking scalar fields.

Contribution

It introduces a 2D gravity approach to study black 3-branes and derives their entropy via a finite central charge, connecting higher-dimensional AdS/CFT to a 2D duality with symmetry breaking.

Findings

Entropy scales as T^3 with temperature.

A finite central charge is obtained after renormalization.

The model illustrates finite temperature effects in AdS/CFT via AdS2/CFT1 duality.

Abstract

A two-dimensional (2D) scalar-tensor gravity theory is used to describe the near-horizon near-extremal behavior of black 3-branes solutions of type IIB string theory. The asymptotic symmetry group of the 2D, asymptotically anti de Sitter (AdS) metric, is generated by a Virasoro algebra. The (non-constant) configuration of the 2D scalar field, which parametrizes the volume of the 3-brane, breaks the conformal symmetry and produces a divergent central charge in the Virasoro algebra. Using a renormalization procedure we find a finite value for the central charge and by means of the Cardy formula, the entropy of the black 3-brane in terms of microstates of the conformal field theory living on the boundary of the 2D spacetime. We find for the entropy as a function of the temperature the power-law behavior $S\propto T^3$. Unfortunately, owing to a scale symmetry of the 2D model the proportionality constant is undetermined. The black 3-brane case is a nice example of how finite temperature effects in higher dimensional AdS/CFT dualities can be described by a AdS$_2$/CFT$_1$ duality endowed with a scalar field that breaks the conformal symmetry and produces a non-vanishing central charge.