Modified Abelian Gauge Theories

TL;DR

This paper introduces a method to modify the topological classes of Abelian p-form gauge fields, creating new global variants with additional charges and anomalies, by constraining their classifying spaces via homotopy fiber construction.

Contribution

It develops a general framework to impose constraints on gauge field topologies, revealing new topological sectors and global charges in Abelian gauge theories.

Findings

New topological sectors with additional global charges

Introduction of anomalies in modified gauge theories

Framework applicable to various Abelian p-form fields

Abstract

The topological properties of field configurations in gauge theory contain important data about the (generalized) global symmetries of the theory as well as potential inconsistencies in the form of gauge anomalies. In this work we modify the topological classes of Abelian $p$-form fields, generating new global variants of gauge theories. These modifications implement constraints directly on the classifying space of the gauge field and its cohomology classes via homotopy fiber construction. This general approach allows us to investigate the universal effects of the constraints on the conserved global charges encoded in gauge characteristic classes. We further demonstrate that this procedure generically leads to new topological sectors introducing additional global charges and anomalies in the modified gauge theories.