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
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
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
