Gauge theory generalization of the fermion doubling theorem

It is possible to characterize certain states of matter by properties of their edge states. This implies a notion of surface-only models: models which can only be regularized at the edge of a higher-dimensional system. After incorporating the fermion-doubling results of Nielsen and Ninomiya into this framework, we employ this idea to identify new obstructions to symmetry-preserving regulators of quantum field theory. We focus on an example which forbids regulated models of Maxwell theory with manifest electromagnetic duality symmetry.