Comments on supergravity dual of pure N=1 Super Yang Mills theory with unbroken chiral symmetry

TL;DR

The paper investigates the gravity dual of a pure $N=1$ Yang–Mills theory with unbroken $U(1)_R$ chiral symmetry by examining type IIB string theory on resolved conifolds with torsion. It derives the SUSY conditions for torsionful vacua, shows that supersymmetric backgrounds on the resolved conifold with nonzero torsion are generically naked singularities, and re-derives the simple singular CV–MN background as the chirally symmetric phase. It then constructs nonsingular non-extremal (finite-temperature) deformations that exhibit a regular horizon, providing a potential holographic mechanism for chiral symmetry restoration at finite temperature, while ensuring UV consistency with the extremal CV–MN solution. The work highlights the relevance of UV completion via deformed conifold geometries for realizing the chirally broken phase and outlines open questions about the exact form of non-extremal solutions and their thermodynamics.

Abstract

Maldacena and Nunez [hep-th/0008001] identified a gravity solution describing pure N=1 Yang-Mills (YM) in the IR. Their (smooth) supergravity solution exhibits confinement and the U(1)_R chiral symmetry breaking of the dual YM theory, while the singular solution corresponds to the gauge theory phase with unbroken U(1)_R chiral symmetry. In this paper we discuss supersymmetric type IIB compactifications on resolved conifolds with torsion. We rederive singular background of [hep-th/0008001] directly from the supersymmetry conditions. This solution is the relevant starting point to study non-BPS backgrounds dual to the high temperature phase of pure YM. We construct the simplest black hole solution in this background. We argue that it has a regular Schwarzschild horizon and provides a resolution of the IR singularity of the chirally symmetric extremal solution as suggested in [hep-th/0011146].