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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.
Kravec et al. (Wed,) studied this question.
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