Non-perturbative analysis, Gribov horizons and the boundary of the fundamental domain

TL;DR

This paper explores the construction of the Gribov horizon and fundamental domain boundary in SU(2) gauge theory, focusing on low energy modes and gauge invariance, highlighting the role of boundary identifications as remnants of Gribov copies.

Contribution

It provides a detailed non-perturbative analysis of the Gribov horizon and fundamental domain boundary in SU(2) gauge theory with a focus on low energy modes and gauge invariance.

Findings

Explicit construction of the Gribov horizon in spherical geometry

Identification of boundary conditions as remnants of Gribov copies

Clarification of the fundamental domain's role in gauge invariance

Abstract

In this contribution to the proceedings we will describe some of the details for constructing the Gribov horizon and the boundary of the fundamental modular domain, when restricting to some low energy modes of pure SU(2) gauge theory in a spherical spatial geometry. The fundamental domain is a one-to-one representation of the set of gauge invariant degrees of freedom, in terms of transverse gauge fields. Boundary identifications are the only remnants of the Gribov copies.