Non-Invertible Duality Defects in 3+1 Dimensions
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 lattice gauge theory.
Cite
@article{arxiv.2111.01139,
title = {Non-Invertible Duality Defects in 3+1 Dimensions},
author = {Yichul Choi and Clay Cordova and Po-Shen Hsin and Ho Tat Lam and Shu-Heng Shao},
journal= {arXiv preprint arXiv:2111.01139},
year = {2022}
}
Comments
41 pages, 8 figures, 1 table. v2: clarifications to defect orientations; references added. v3: major changes in section 3