Boundary electromagnetic duality from homological edge modes

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.