Boundary electromagnetic duality from homological edge modes

TL;DR

This paper explores electromagnetic duality at boundaries using homological methods, revealing dual edge modes as connections over a (-1)-gerbe and linking the central charge to its non-trivial class.

Contribution

It introduces a homotopy pullback and Deligne-Beilinson cohomology framework to describe boundary electromagnetic duality and identifies dual edge modes as (-1)-gerbe connections.

Findings

Dual edge modes are connections over a (-1)-gerbe.

The central charge is related to a non-trivial class of the (-1)-gerbe.

Boundary duality is implemented via a BF-like topological boundary term.

Abstract

Recent years have seen a renewed interest in using `edge modes' to extend the pre-symplectic structure of gauge theory on manifolds with boundaries. Here we further the investigation undertaken in \cite{FP2018} by using the formalism of homotopy pullback and Deligne-Beilinson cohomology to describe an electromagnetic (EM) duality on the boundary of $M=B^{3}\times\mathbb{R}$. Upon breaking a generalized global symmetry, the duality is implemented by a BF-like topological boundary term. We then introduce Wilson line singularities on $\partial M$ and show that these induce the existence of dual edge modes, which we identify as connections over a $\left(-1\right)$-gerbe. We derive the pre-symplectic structure that yields the central charge in \cite{FP2018} and show that the central charge is related to a non-trivial class of the $\left(-1\right)$-gerbe.