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arXiv · 2111.01139

Non-Invertible Duality Defects in 3+1 Dimensions

Yichul Choi·Clay Cordova·Po-Shen Hsin·Ho Tat Lam·Shu-Heng Shao
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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.

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Yichul Choi, Clay Cordova, Po-Shen Hsin, Ho Tat Lam, Shu-Heng Shao. 2022-05-04. Non-Invertible Duality Defects in 3+1 Dimensions. https://doi.org/10.1103/physrevd.105.125016

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