Finite Temperature Effects in the Supergravity Dual of the N=1* Gauge Theory

TL;DR

This paper investigates the finite temperature effects in the supergravity dual of the N=1* gauge theory, analyzing the behavior of 5-branes, back reactions, and entropy corrections across different temperature regimes.

Contribution

It provides a detailed analysis of the supergravity dual at finite temperature, including the back reaction of hypermultiplet mass and the phase transition behavior.

Findings

Existence of a critical temperature separating high and low temperature phases.

Entropy correction due to mass effects is negative and smaller than free field predictions.

At high temperature, 5-branes are not required as no naked singularities are present.

Abstract

We consider the supergravity dual of the N=1* theory at finite temperature by applying the Polchinski-Strassler construction to the black D3 brane solution of Type IIB supergravity. At finite temperature the 5-brane probe action is minimized when the probe falls to the horizon, although metastable minima with r>>r_H persist for a range of temperatures. Thermal effects on the 3-form source for the hypermultiplet mass m and its order m^2 back reaction on the other fields of the IIB theory are computed. We find unique solutions which are regular at the horizon and have the correct behavior on the boundary. For fixed temperature T, the horizon shrinks for increasing m^2 suggesting that there is a critical temperature separating the system into high and low temperature phases. In the high temperature phase 5-branes are unnecessary since there are no naked singularities. Using the order m^2 correction to the horizon area we calculate the correction to the entropy to be \Delta S =-0.1714N^2m^2T, which is less than the free field result.