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

TL;DR

The paper explores finite-temperature holography for the N=1* gauge theory by embedding Polchinski-Strassler deformations into a black D3-brane background. It computes the linear 3-form perturbation and the fully backreacted dilaton, metric, and 5-form fields to order $m^2$, showing that the horizon area decreases and yielding a finite-temperature entropy correction $\Delta\mathcal{S} = -0.1714\,N^2\,m^2\,T$. The analysis reveals metastable 5-brane vacua at finite temperature, a horizon-centric high-temperature phase, and a proposed critical temperature $T_c$ signaling a phase transition. The results provide a quantitative link between strong-coupling holographic thermodynamics and the mass-deformed ${\cal N}=4$ theory, with implications for confining dynamics and phase structure in the dual gauge theory.

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 ΔS =-0.1714N^2m^2T, which is less than the free field result.