A 4D TQFT which is not (quite) a gauge theory

Abstract: Some people have accused me of proving that every (nice enough) 4D TQFT is equivalent to a gauge theory. A version of this statement is true, but only if your notion of "gauge theory" allows dynamical spin structures among the "gauge fields", and some rather complicated terms in the Lagrangian that couple the spin structures to the other gauge fields. That said, many of these 4D TQFTs also admit "dual" descriptions as true gauge theories for higher-form groups. In this talk, I will explain exactly which 4D TQFTs are equivalent to true (higher-group) gauge theories theories, and present a minimal counterexample to the belief that all 4D TQFTs are true gauge theories.

MathematicsPhysics

Audience: researchers in the topic

Symmetry Seminar

Series comments: Weekly seminar on generalized symmetries in QFT, string theory and related topics.