Confinement and chiral symmetry breaking in holography: a smooth switch-off

TL;DR

This paper explores the holographic phase transition in N=4 SYM, showing a smooth transition from confinement to deconfinement and chiral symmetry restoration via a continuous geometric interpolation.

Contribution

It constructs a family of geometries describing the unstable transition branch, revealing a continuous switch-off of confinement and chiral symmetry breaking.

Findings

Confinement persists along the unstable branch with decreasing string tension.

Chiral condensate decreases smoothly and vanishes at the deconfinement point.

The transition involves a continuous geometric interpolation between phases.

Abstract

We revisit the holographic description of the thermal first order phase transition of N=4 SYM compactified on a spatial circle. At the transition, the dominant bulk saddle exchanges between a geometry with a compact spatial circle and one with a compact Euclidean time circle. We construct a one-parameter family of Euclidean geometries that describes the unstable branch of the transition, completing the swallow-tail structure of the free energy. Although these configurations are thermodynamically unstable, they provide a continuous interpolation between the confining soliton and the deconfined black hole phases. Using probe fundamental strings, we show that the theory remains confining along the unstable branch, with a string tension that decreases smoothly and vanishes only in the black hole limit. Introducing fundamental matter via probe D5-branes, we find that chiral symmetry breaking follows the same pattern: the condensate decreases continuously and switches off precisely where confinement disappears. We discuss the implications for the confinement and chiral symmetry breaking mechanisms at large Nc.