Fuzzy spheres at finite temperature supported by Wilson lines

TL;DR

This paper investigates how finite temperature affects fuzzy sphere solutions in a specific gauge theory, showing thermal effects shrink the sphere and that background gauge fields can stabilize and induce symmetry-breaking phases.

Contribution

It demonstrates that thermal effects diminish fuzzy sphere size and introduces a method to stabilize them using Wilson lines, revealing a persistent baryonic symmetry-breaking phase at finite temperature.

Findings

Thermal effects reduce the fuzzy sphere radius to zero.

Adding Wilson lines stabilizes the fuzzy sphere at finite temperature.

A phase with broken baryonic symmetry persists at weak coupling.

Abstract

We study the fate of the fuzzy sphere vacuum solutions in the SU(N)xSU(N+M) Klebanov-Strassler theory at finite temperature and at weak coupling. We find that thermal effects push the S^2 radius --a modulus at T=0-- towards vanishing size. We then show that the fuzzy sphere can be stabilized by adding a temporal Wilson line for a background U(1) gauge field, which can be associated with either the baryonic or the R-symmetry. Thus, upon deforming the KS theory with a background gauge field for a global symmetry, we find a phase of broken baryonic symmetry at weak coupling surviving at finite temperature.