A gauge theory generalization of the fermion-doubling theorem

TL;DR

The paper investigates obstructions to symmetry-preserving regulators of 3+1D QFTs by embedding the problem in 4+1D gapped bulk TFTs whose surface theories—surface-only models—signal when a symmetry cannot be preserved by any local regulator.The authors study a simple 4+1D theory built from 2-form gauge fields with a K-matrix, analyze the bulk ground-state degeneracy via the intersection form, and determine when the bulk describes a bosonic SRE phase versus a bulk with topological order.A central result is that the boundary of the 4+1D abelian two-form theory reduces to Maxwell theory on the boundary, but maintaining manifest EM duality in a local regulator is impossible; breaking the duality requires coupling to charged boundary matter, implying EM duality cannot be gauged in Maxwell theory.The work situates these observations within a broader framework of higher-dimensional CS theories, connections to the (2,0) theory, and the interpretation of surface obstructions as potential anomalies, raising questions about the generality of the anomaly perspective for surface-only models.

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.

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