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Geometry and Physics Seminar 2021 Fall
Non-invertible topological defects in 4-dimensional $Z_2$ pure lattice gauge theory
Non-invertible topological defects in 4-dimensional $Z_2$ pure lattice gauge theory
Organizer
Speaker
Satoshi Yamaguchi
Time
Tuesday, November 16, 2021 11:00 AM - 1:00 PM
Venue
1120
Online
Zoom 388 528 9728
(BIMSA)
Abstract
Recently, there has been progress in extending the concept of symmetry by using the notion of topological defects. One of such new symmetries is so-called "non-invertible symmetry." In 2 dimensions, non-invertible symmetries are investigated actively and shown to be a powerful tool. On the other hand, non-invertible symmetries in higher dimensions are less understood than those in 2 dimensions. In this talk, we explore topological defects in the 4-dimensional pure $Z_2$ lattice gauge theory. This theory has 1-form $Z_2$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality topological defects and $Z_2$ center symmetry defects in a similar way to those constructed by Aasen, Mong, Fendley for the 2-dimensional Ising model. These duality defects turn out to be non-invertible. In other words, the KWW duality is not a symmetry in the traditional sense, but a non-invertible symmetry. We also construct the junctions among these topological 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.