Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Masataka Koide; Yuta Nagoya; Satoshi Yamaguchi

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arXiv · 2109.05992

Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory

Masataka Koide·Yuta Nagoya·Satoshi Yamaguchi

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Abstract

We explore topological defects in the 4-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb{Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality topological defects in the similar way to that constructed by Aasen, Mong, Fendley arXiv:1601.07185 for the 2-dimensional Ising model. These duality defects turn out to be non-invertible. We also construct the 1-form $\mathbb{Z}_{2}$ symmetry defects as well as the junctions among KWW duality defects and 1-form $\mathbb{Z}_{2}$ center symmetry defects. The crossing relations among these defects are derived. The expectation values of some configurations of these topological defects are calculated by using these crossing relations.

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Masataka Koide, Yuta Nagoya, Satoshi Yamaguchi. 2021-09-13. Non-invertible topological defects in 4-dimensional $\mathbb{Z}_2$ pure lattice gauge theory. https://arxiv.org/abs/2109.05992

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