Dynamics on the SU(2) fundamental domain

TL;DR

This paper investigates the energy landscape and tunneling phenomena in SU(2) gauge theory on a three-sphere, focusing on a specific mode subspace to understand the $ heta$-dependence of low-energy states.

Contribution

It identifies a degenerate subspace of gauge field modes containing tunneling paths and sphalerons, facilitating the study of $ heta$-dependence in SU(2) gauge theory.

Findings

Characterization of a subspace with degenerate energy functional

Identification of tunneling paths and sphalerons within this subspace

Foundation for studying $ heta$-dependence of low-lying states

Abstract

For SU(2) gauge theory on the three-sphere we focus on a subspace of modes of the gauge field that contains the tunnelling paths and the sphalerons and on which the energy functional is degenerate to second order in the fields. The ultimate goal is to study the $\theta$-dependence of the low-lying states for this model by imposing boundary conditions on the fundamental domain.