A non-abelian duality for (higher) gauge theories

TL;DR

This paper explores dualities in higher gauge theories by analyzing a topological field theory on a manifold with boundaries, revealing known and new dualities such as electric-magnetic and Poisson-Lie T-duality.

Contribution

It introduces a framework for understanding dualities in higher gauge theories via boundary conditions in topological field theories, including new higher analogues.

Findings

Recovered electric-magnetic duality.

Revealed Poisson-Lie T-duality.

Discovered new higher gauge theory dualities.

Abstract

We consider a TFT on the product of a manifold with an interval, together with a topological and a non-topological boundary condition imposed at the two respective ends. The resulting (in general higher gauge) field theory is non-topological, with different choices of the topological conditions leading to field theories dual to each other. In particular, we recover the electric-magnetic duality, the Poisson-Lie T-duality, and we obtain new higher analogues thereof.