A lattice construction of 2d Spin Topological Field Theories

9 December 2013
Sebastian Novak
TQFTs have received widespread attention in recent years. In mathematics for example due to Lurie's proof of the cobordism hypothesis. In physics they are used as toy models to understand structure, especially boundaries and defects. I will present a lattice construction of 2d Spin TFT. This mostly motivated as both a toy model and stepping stone for a mathematical construction of rational conformal field theories with fermions. I will first describe a combinatorial model for spin surfaces that consists of a triangulation and a finte set of extra data. This model is then used to construct TFT correlators as morphisms in a symmetric monoidal category, given a Frobenius algebra as input. The result is shown to be independent of the triangulation used, and one obtains thus a 2dTFT. All results and constructions can be generalised to framed surfaces in a relatively straightforward way.
  • Junior Geometry and Topology Seminar