Non-Invertible Duality Defects in 3+1 Dimensions

TL;DR

This paper constructs non-invertible topological defects in 3+1D gauge theories by half-spacetime gauging, generalizing dualities and revealing their incompatibility with trivial gapped phases, with explicit realizations in Maxwell and lattice models.

Contribution

It introduces a novel method to create non-invertible duality defects in higher dimensions and provides explicit models and fusion rules for these defects.

Findings

Constructed duality defects in 3+1D gauge theories.

Showed duality defects are incompatible with trivial gapped phases.

Explicit realizations in Maxwell and lattice gauge theories.

Abstract

For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions, and determine the fusion rule. From a direct analysis of one-form symmetry protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. We give an explicit realization of this duality defect in the free Maxwell theory, both in the continuum and in a modified Villain lattice model. The duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides. We further construct the duality defect in non-abelian gauge theories and the $\mathbb{Z}_N$ lattice gauge theory.