Dyonic edge modes in Abelian gauge theory

We find new boundary conditions in four-dimensional Abelian gauge theory with general Chern–Simons boundary couplings. The boundary conditions allow dyonic edge modes and physical boundary symmetries. In particular, one of the new boundary conditions makes both electric and magnetic charges physical. We also study how our boundary conditions and charges transform under the $\mathrm{S}\mathrm{L}(2,\mathbb{Z})$ duality.