April 12, 2022

Speaker: Ho Tat Lam (MIT)

Title: Non-invertible Condensation, Duality and Triality Defects in 3+1d

Abstract: We discuss a variety of non-invertible topological defects in 3+1d. These include the condensation defects defined by gauging a one-form symmetry on a codimension-one manifold, and the duality and triality defects defined for systems invariant under gauging a one-form symmetry. We determine their universal fusion rules and emphasize that the fusion coefficients are generally not a number but the partition functions of TQFTs. From a direct analysis of one-form symmetry protected topological phases, we show that the existence of certain kinds of non-invertible defects is intrinsically incompatible with a trivially gapped phase, leading to nontrivial constraints on renormalization group flow. We give an explicit realization of these non-invertible defects in the free Maxwell theory using Chern-Simons coupling.