Speaker
Description
In recent years we have learned that several four-dimensional field theories can manifest non-invertible zero-form symmetries generalizing the Kramers-Wannier duality defect of the 2d critical Ising model. Several recent works by various groups have observed a deep interplay among such non-invertible symmetries in 3+1 dimensions, their anomalies, and the properties of the ground state(s). In this talk I will review these developments and present a first coarse classification of non-invertible symmetries of this type that can either enforce gaplessness or be spontaneously broken in the infrared exploiting the topological symmetry theory formalism. The methods presented also generalize to non-invertible KW-like duality symmetries graded by non-abelian finite subgroups. I will present examples in the context of supersymmetric models and, along the way, I will notice the potential for further global structures that could be realized by non-SUSY versions of Argyres-Douglas type fixed points.
