Randall-Sundrum Model with a Dilaton Field at Finite Temperature

TL;DR

This paper derives exact finite temperature solutions in a 5D Einstein-dilaton model with a Randall-Sundrum brane, analyzing their thermodynamics and dual gauge theory behavior, including a limit reducing to finite-temperature $ ext{N}=4$ SYM.

Contribution

It provides the first exact finite temperature solutions with a Randall-Sundrum brane in Einstein-dilaton gravity and explores their thermodynamics and gauge duals.

Findings

Existence of a unique superpotential for these models.

Black brane location and temperature depend on brane tension.

Entropy is less than the standard black hole entropy.

Abstract

We find exact finite temperature solutions to $d=5$ Einstein-dilaton gravity with black branes and a Randall--Sundrum 3-brane. We show that there exists a unique generating superpotential for these models. The location of the black brane and the associated Hawking temperature depend on the value of the the 3-brane tension while other parameters are held fixed. The thermodynamics of these solutions are presented, from which we show that the entropy satisfies $S<\text{Vol}(\mathbb{R}^3)/4G_5$. We demonstrate that in a certain limit the gauge dual of this theory effectively reduces to $\mathcal{N}=4$ SYM at finite temperature on $S^1\times\mathbb{R}^3$