Symmetry breaking caused by large R-charge

TL;DR

This paper investigates how large R-charge induces gauge symmetry breaking via the Hosotani mechanism in supersymmetric theories on curved space, revealing phase structure and finite size effects.

Contribution

It demonstrates the necessity of large R-charge for symmetry breaking and analyzes the phase structure using exact localization results on S^2 x S^1.

Findings

Large R-charge is essential for gauge symmetry breaking.

Finite size effects are minimal at large R-charge.

Phase structure depends on the R-charge and chemical potential.

Abstract

We discuss the gauge symmetry breaking via the Hosotani mechanism by using exact results on supersymmetric gauge theories based on the localization method. We use the theories on S^2 x S^1 Euclidean space, and study how the effective potential for the Wilson line phase varies by running an imaginary chemical potential. In order to break the symmetry, we find that large R-charge is necessary. With such large R-charge, we study the phase structure of the theory. In addition, we observed that a finite size effect on our curved space when we take R-charge is not so large.