Spin-statistics and unitarity for low-dimensional topological field theories

For zoom details contact Peter Teichner (teichner@mpim-bonn.mpg.de) or David Reutter.

Unitarity and the spin-statistics connection play an important role in relativistic quantum field theory. Recently these concepts have begun to be explored mathematically in the context of topological field theory. In joint work with Lukas Müller, I provide explicit classifications of such TFTs with various symmetry groups in spacetime dimension two. On the one hand, we find that assuming a spin-statistics connection or unitarity makes the computations more transparent. On the other hand, the formalism recovers well-known physical phenomena like the fact that time-reversing symmetries act anti-unitarily on Hilbert space. I will explain the main techniques and results in spacetime dimension one, in particular the role of fixed points of group actions on categories in the cobordism hypothesis. Towards the end, I will sketch the generalization to dimension two.