Topological Defects in a Deformed Gauge Theory

TL;DR

This paper investigates how a minimal length scale deformation in a non-abelian gauge theory affects topological defects, using Polyakov variables to analyze the resulting deformed loop space curvature and Bianchi identities.

Contribution

It introduces a framework for analyzing topological defects in deformed gauge theories via Polyakov loops and explores how background geometry deformation influences topological structures.

Findings

Deformed loop space curvature vanishes when deformed Bianchi identities hold.

Violations of deformed Bianchi identities can occur at leading order, indicating topological defects.

Topological defects can emerge purely from background geometry deformation.

Abstract

In this paper, we will analyse the topological defects in a deformation of a non-abelian gauge theory using the Polyakov variables. The gauge theory will be deformed by the existence of a minimum measurable length scale in the background spacetime. We will construct the Polyakov loops for this deformed non-abelian gauge theory, and use these deformed loop space variables for obtaining a deformed loop space curvature. It will be demonstrated that this curvature will vanish if the deformed Bianchi identities are satisfied. However, it is possible that the original Bianchi identities are satisfied, but the deformed Bianchi identities are violated at the leading order in the deformation parameter, due to some topological defects. Thus, topological defects could be produced purely from a deformation of the background geometry.