Generalized Hedgehog ansatz and Gribov copies in regions with non trivial topologies

TL;DR

This paper explores the existence of Gribov copies in gauge theories within regions of non-trivial topology, introducing a generalized hedgehog ansatz to construct explicit examples and analyze geometrical constraints.

Contribution

It presents a novel generalization of the hedgehog ansatz beyond spherical symmetry to construct Gribov copies analytically in flat topological regions.

Findings

Constructed explicit Gribov copies of the vacuum

Identified geometrical constraints on region shapes and sizes

Introduced the elliptic Gribov pendulum

Abstract

In this paper the arising of Gribov copies both in Landau and Coulomb gauges in regions with non-trivial topologies but flat metric, (such as closed tubes S1XD2, or RXT2) will be analyzed. Using a novel generalization of the hedgehog ansatz beyond spherical symmetry, analytic examples of Gribov copies of the vacuum will be constructed. Using such ansatz, we will also construct the elliptic Gribov pendulum. The requirement of absence of Gribov copies of the vacuum satisfying the strong boundary conditions implies geometrical constraints on the shapes and sizes of the regions with non-trivial topologies.