Topological self-dual vacua of deformed gauge theories

TL;DR

This paper introduces a deformation principle for three-dimensional gauge theories that admits topologically stable, self-dual vacua, which are undetectable locally and relate to boundary phenomena of higher-dimensional self-dual fields.

Contribution

It proposes a novel deformation approach for gauge theories that captures self-dual vacua and boundary degrees of freedom, extending to higher dimensions and p-form connections.

Findings

Identification of topologically stable self-dual vacua in deformed gauge theories

Connection between these vacua and boundary degrees of freedom of higher-dimensional fields

Proposal of generalizations to higher dimensions and p-form gauge connections

Abstract

We propose a deformation principle of gauge theories in three dimensions that can describe topologically stable self-dual gauge fields, i.e., vacua configurations that in spite of their masses do not deform the background geometry and are locally undetected by charged particles. We interpret these systems as describing boundary degrees of freedom of a self-dual Yang-Mills field in $2+2$ dimensions with mixed boundary conditions. Some of these fields correspond to Abrikosov-like vortices with an exponential damping in the direction penetrating into the bulk. We also propose generalizations of these ideas to higher dimensions and arbitrary p-form gauge connections.