Lagrangian structures on mapping stacks and semi-classical TFTs

Understand

We extend a recent result of Pantev-Toen-Vaquie-Vezzosi, who constructed shifted symplectic structures on derived mapping stacks having a Calabi-Yau source and a shifted symplectic target.

• Their construction gives a clear conceptual framework for the so-called AKSZ formalism.
• We extend the PTVV construction to derived mapping stacks with boundary conditions, which is required in most applications to quantum field theories (see e.g.
• the work of Cattaneo-Felder on the Poisson sigma model, and the recent work of Cattaneo-Mnev-Reshetikhin).