Kramers-Wannier-like Duality Defects in (3+1)D Gauge Theories.

Justin Kaidi,Kantaro Ohmori,Yunqin Zheng

doi:10.1103/physrevlett.128.111601

Justin Kaidi, Kantaro Ohmori + Show 1 more

Open Access

https://doi.org/10.1103/physrevlett.128.111601

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Abstract

We introduce a class of noninvertible topological defects in (3+1)D gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1+1)D critical Ising model. As in the lower-dimensional case, the presence of such noninvertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ=π, N=1 SO(3) super YM, and N=4 SU(2) super YM at τ=i. We also introduce an analogous construction in (2+1)D, and give a number of examples in Chern-Simons-matter theories.

Highlights

We introduce a class of noninvertible topological defects in ð3 þ 1ÞD gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the ð1 þ 1ÞD critical Ising model
The prototypical example of such a symmetry is the one arising from the Kramers-Wannier self-duality of the ð1 þ 1ÞD Ising model at the critical point
This means that one must extend the notion of symmetry beyond groups, leading in ð1 þ 1ÞD to a mathematical construction known as a fusion category [6–8]

Summary

Yunqin Zheng

We introduce a class of noninvertible topological defects in ð3 þ 1ÞD gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the ð1 þ 1ÞD critical Ising model. Recent developments have led to several extensions of the notion of global symmetry One such example is higher-form symmetry [1], which has had numerous applications such as constraining the IR phases of pure Yang-Mills (YM) theory [2]. The basic idea of noninvertible symmetry is to consider any topological defect as a form of generalized symmetry This means that one must extend the notion of symmetry beyond groups, leading in ð1 þ 1ÞD to a mathematical construction known as a fusion category [6–8]. We illustrate the existence of these defects and their potential dynamical applications through the example of

Published by the American Physical Society

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