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 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.

• MO
  Ministry of Education, Culture, Sports, Science and Technology
• UO
  University of Tokyo