| Abstract: |
I describe an axiomatic formulation of QFT (following Segal, Atiyah, and Kontsevich) using bordism and the language of infinity categories. In this language, QFTs are collectively assembled into a generalized space, whose (higher) homotopy groups encode (generalized) symmetries of QFTs. In this picture, 't Hooft anomalies can be understood as a failure to respect locality. A new kind of anomaly arises, which can be understood as a failure to respect smoothness; an example occurs already in the quantum mechanics of a two-state system. |
