Non-Invertible Duality Interfaces in Field Theories with Exotic Symmetries

TL;DR

This paper explores the interplay of exotic and non-invertible symmetries in various field theories, revealing new duality interfaces and their fusion rules, with implications for understanding generalized global symmetries.

Contribution

It introduces novel duality interfaces in theories with exotic and non-invertible symmetries, analyzing their fusion rules and dependence on UV cutoff, expanding the understanding of generalized symmetries.

Findings

Fusion rules are condensation defects from higher gauging exotic symmetries.

Duality interfaces constructed via gauging and duality transformations.

Dependence of symmetry properties on UV cutoff addressed.

Abstract

In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse according to a group law. Only recently has the interplay between these two been examined. In this paper, we provide further examples of the interplay in the XY plaquette model, XY cube model, 1+1 d theory with global dipole symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of the momentum symmetry on half of spacetime and then performing a duality transformation. We analyze the fusion rules of the symmetries and find that they are condensation defects from an analog of higher gauging exotic symmetries. We also address their dependence on the UV cutoff when relevant.