Speaker: Ryohei Kobayashi (IAS)
Title: Â Soft symmetries of topological orders
Abstract: (2+1)D topological orders possess emergent symmetries that consists of the braided tensor autoequivalences of the modular tensor category. In this talk we discuss cases where symmetries neither permute anyons nor are associated to any symmetry fractionalization but are still non-trivial, which we refer to as soft symmetries. We point out that one can construct topological defects corresponding to such exotic symmetry actions by decorating with a certain class of gauged SPT states that cannot be distinguished by their torus partition function. This gives a physical interpretation to work by Davydov on soft braided tensor autoequivalences. This has a number of important implications for the classification of gapped boundaries, non-invertible spontaneous symmetry breaking, and the general classification of symmetry-enriched topological phases of matter. We also demonstrate analogous phenomena in higher dimensions, such as (3+1)D gauge theory with gauge group given by the quaternion group Q8.