Chiral symmetry breaking and inhomogeneous phases in thermal anti-de Sitter spacetime

TL;DR

This paper investigates how chiral symmetry breaking in a quark-meson model within thermal anti-de Sitter spacetime depends on temperature and curvature, revealing a phase diagram with competing effects.

Contribution

It provides a detailed analysis of inhomogeneous condensates and the phase structure considering the Hawking-Page transition in AdS.

Findings

Chiral symmetry is always broken near the AdS boundary.

Temperature tends to restore chiral symmetry, while negative curvature promotes breaking.

The phase diagram depends critically on AdS curvature and temperature, with a unique regular solution for the condensate.

Abstract

We study the spontaneous breaking of chiral symmetry in an AdS spacetime at finite temperature using the quark-meson model. The condensate $\sigma$ is typically inhomogeneous in AdS and is determined from the differential gap equation. We demonstrate that there are no free integration constants in the regular solutions to the differential equation and find that the solution to the boundary value problem is unique. We find that chiral symmetry is always broken close to the AdS boundary. We construct the phase diagram of the system as a function of the AdS curvature and temperature. These two parameters have opposing effects: temperature tends to restore chiral symmetry, whereas negative curvature favors its spontaneous breaking. We also consider how the phase diagram is modified when the Hawking-Page phase transition is taken into account.