Kramers-Wannier-like duality defects in (3+1)d gauge theories

TL;DR

This paper introduces non-invertible topological defects in (3+1)d gauge theories, revealing new duality structures and self-duality properties, with examples in various Yang-Mills theories and an analogous (2+1)d construction.

Contribution

It constructs higher-dimensional non-invertible defects in gauge theories, extending the concept of Kramers-Wannier duality defects to (3+1)d and (2+1)d contexts.

Findings

Existence of non-invertible defects in (3+1)d gauge theories.

Self-duality under discrete higher-form symmetry gauging.

Examples include SO(3) and SU(2) super Yang-Mills theories.

Abstract

We introduce a class of non-invertible topological defects in (3+1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1+1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at $\theta = \pi$, $\mathcal{N}=1$ SO(3) super YM, and $\mathcal{N}=4$ SU(2) super YM at $\tau = i$. We also introduce an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories.