CMSA Quantum Field Theory and Physical Mathematics Seminar: BV and the ThimTFT

he SymTFT (or “quiche”) construction relates different global forms of d-dimensional QFTs with discrete symmetry: realizing different global forms as a (d+1)-dimensional TFT on an interval, with a common “physical” boundary condition on one side, and different topological boundary conditions on the other. In my talk, I will describe an analogue of the SymTFT which relates theories with the same “perturbative equations of motion,” but different non-perturbative completions.

I will start with a lightning overview of conformal blocks and relative QFT, then explain the BV formalism in some detail — focusing on the elegant (super)geometric story in 0d for simplicity. I will argue that there is a natural 1d cohomological TFT (called the ThimTFT) associated to the classical action S, with different topological boundary conditions described by convergent path-integral contours in a complexified field space. Time permitting, I will discuss extensions to higher dimensions. Based on WIP.

In person and online: