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We introduce a class of non-invertible topological defects in (3+1)d gaugetheories whose fusion rules are the higher-dimensional analogs of those of theKramers-Wannier defect in the (1+1)d critical Ising model. As in thelower-dimensional case, the presence of such non-invertible defects impliesself-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 $\theta = \pi$, $\mathcal{N}=1$ SO(3) super YM, and $\mathcal{N}=4$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.

Kramers-Wannier-like duality defects in (3+1)d gauge theories