Phase structure of compactified $SU(N)$ gauge theories in magnetic backgrounds

TL;DR

This paper explores how $SU(N)$ gauge theories behave when compactified with magnetic backgrounds, revealing various phase structures influenced by the compactification radius and magnetic field, supported by lattice simulations.

Contribution

It introduces an analysis of phase structures in non-abelian gauge theories with magnetic backgrounds, including new numerical lattice results for $SU(3)$ with fundamental fermions.

Findings

Different phases depend on compactification radius and magnetic field strength.

Center symmetry and translational invariance can be broken or preserved in various phases.

Preliminary lattice results support the theoretical phase structure analysis.

Abstract

We discuss the properties of non-abelian gauge theories formulated on manifolds with compactified dimensions and in the presence of fermionic fields coupled to magnetic backgrounds. We show that different phases may emerge, corresponding to different realizations of center symmetry and translational invariance, depending on the compactification radius and on the magnitude of the magnetic field. Our discussion focuses on the case of an $SU(3)$ gauge theory in 4 dimensions with fermions fields in the fundamental representation, for which we provide some exploratory numerical lattice results.