Geometry and Physics Seminar

Symmetry-protected topological phases of matter (SPTs) admit descriptions in terms of homotopy theory. Freed--Hopkins defined "free-to-interacting maps" to model the physical process of comparing free fermion SPTs (classified by K-theory) with more general, interacting models (classified by certain invertible functorial field theories). With Debray and Stehouwer, we generalized this approach to study the "Bott spiral" of SPTs constructed by Queiroz--Khalaf--Stern. After reviewing the homotopical classification of invertible field theories, I will discuss our construction and some subtleties that arise in defining free-to-interacting maps, such as compatibility with dimensional reduction, continuous versus discrete symmetry types, and the lack of interacting Morita invariance.