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Non-Invertible Duality Defects in 3+1 Dimensions

High Energy Physics - Theory 2022-07-13 v3 Strongly Correlated Electrons Mathematical Physics math.MP

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 ZN\mathbb{Z}_N lattice gauge theory.

Keywords

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

R2 v1 2026-06-24T07:21:29.200Z