On Forms with Non-Abelian Charges and Their Dualities

TL;DR

This paper explores non-Abelian charged forms within topological field theories, deriving dual models and discussing gauge conditions, exemplified by charged two-forms in six dimensions.

Contribution

It introduces a framework for non-Abelian charged forms in TQFTs and constructs dual models without flat curvature constraints.

Findings

Developed TQFTs for forms and their duals

Provided example of charged two-forms in six dimensions

Discussed gauge conditions for dual formulations

Abstract

We describe forms with non-Abelian charges. We avoid the use of theories with flat curvatures by working in the context of topological field theory. We obtain TQFTs for a form and its dual. We leave open the question of getting gauges in which the form, or its dual, can be gauged away, in such way that the model has two dual formulations. We give the example of charged two-forms in six dimensions.