Non-Extremal Gravity Duals for Fractional D3-Branes on the Conifold

TL;DR

This paper investigates non-extremal gravity duals for fractional D3-branes on the conifold, aiming to understand finite temperature effects and chiral symmetry restoration in the dual gauge theory.

Contribution

It constructs an ansatz for non-extremal solutions and demonstrates that the simplest solution has a singular horizon, advancing the understanding of finite temperature duals.

Findings

The simplest non-extremal solution has a singular horizon.

Derived second order equations for potential regular solutions.

Provided a framework for studying chiral symmetry restoration at finite temperature.

Abstract

The world volume theory on $N$ regular and $M$ fractional D3-branes at the conifold singularity is a non-conformal ${\cal N}=1$ supersymmetric $SU(N+M)\times SU(N)$ gauge theory. In previous work the extremal Type IIB supergravity dual of this theory at zero temperature was constructed. Regularity of the solution requires a deformation of the conifold: this is a reflection of the chiral symmetry breaking. To study the non-zero temperature generalizations non-extremal solutions have to be considered, and in the high temperature phase the chiral symmetry is expected to be restored. Such a solution is expected to have a regular Schwarzschild horizon. We construct an ansatz necessary to study such non-extremal solutions and show that the simplest possible solution has a singular horizon. We derive the system of second order equations in the radial variable whose solutions may have regular horizons.