Zooming-in on the SU(2) fundamental domain

TL;DR

This paper investigates the structure of the fundamental domain and Gribov horizon in SU(2) gauge theories on the three-sphere, providing mathematical proofs about their boundary properties in a specific high-dimensional subspace.

Contribution

It offers a rigorous analysis of the boundary of the fundamental domain and its relation to the Gribov horizon in a particular 18-dimensional subspace of SU(2) gauge theories.

Findings

Parts of the boundary coincide with the Gribov horizon.

Provides bounds on the fundamental modular domain.

Analyzes the degenerate energy functional in the subspace.

Abstract

For SU(2) gauge theories on the three-sphere we analyse the Gribov horizon and the boundary of the fundamental domain in the 18 dimensional subspace that contains the tunnelling path and the sphaleron and on which the energy functional is degenerate to second order in the fields. We prove that parts of this boundary coincide with the Gribov horizon with the help of bounds on the fundamental modular domain.