  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.
