A gauge theory generalization of the fermion-doubling theorem

TL;DR

This paper extends the fermion-doubling theorem to surface-only models, revealing new obstructions to regularizing certain gauge theories with symmetry preservation, such as Maxwell theory with electromagnetic duality.

Contribution

It generalizes the fermion-doubling theorem within a framework of surface-only models, identifying novel constraints on symmetry-preserving regularizations of quantum field theories.

Findings

Identifies obstructions to regularizing Maxwell theory with electromagnetic duality.

Extends fermion-doubling concepts to surface-only models.

Reveals new topological constraints on quantum field theory regularization.

Abstract

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.