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

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 theta = pi, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at tau = i. We also introduce an analogous construction in (2 + 1)D, and give a number of examples in ChemSimons-matter theories.

Automated summary

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. Examples include SO(3) Yang-Mills (YM) at theta = pi, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at tau = i. We also introduce an analogous construction in (2 + 1)D, and give a number of examples in Chern-Simons matter theories.