Deligne–Mumford field theories from categories
GAUGE THEORY AND TOPOLOGY
Open-closed Deligne–Mumford field theories (oc-DMFTs) are a variant of 2D topological field theories (TFTs). These are based on moduli spaces of stable nodal curves and encode the algebraic structure of Gromov–Witten invariants. Obtaining TFTs and related structures from suitable categories has been a subject of significant interest. I will explain how to obtain an oc-DMFT from a smooth, proper Calabi–Yau category and a splitting of the non-commutative Hodge–de Rham spectral sequence. This provides an enhancement of the categorical enumerative invariants of Costello and Caldararu–Tu. The construction has a precise universal property that can be used to compare it with the geometrically defined Gromov–Witten oc-DMFT, provided the latter can be constructed.