Flat connections for Yang-Mills theories on the 3--torus

TL;DR

This paper investigates the structure of flat connections in Yang-Mills theories on a three-dimensional torus, revealing multiple components in the moduli space for certain gauge groups, which impacts understanding of gauge theory solutions.

Contribution

It characterizes the moduli space of flat connections on T^3 x R for various gauge groups, highlighting the existence of multiple components for specific groups.

Findings

Multiple components in the moduli space for SO(N>=7), G_2, F_4, E_6, E_7, E_8.

Distinct flat connection classes identified for these gauge groups.

Implications for the vacuum structure in Yang-Mills theories.

Abstract

We discuss the moduli space of flat connections of Yang-Mills theories formulated on T^3 x R, with periodic boundary conditions. When the gauge group is SO(N>=7), G_2, F_4, E_6, E_7 or E_8, the moduli space consists of more than one component.