Poisson AKSZ theories and their quantizations

Abstract

We generalize the AKSZ construction of topological field theories to allow the target manifolds to have possibly-degenerate (homotopy) Poisson structures. Classical AKSZ theories, which exist for all oriented spacetimes, are described in terms of dioperads. The quantization problem is posed in terms of extending from dioperads to properads. We conclude by relating the quantization problem for AKSZ theories on R^d to the formality of the E_d operad, and conjecture a properadic description of the space of E_d formality quasiisomorphisms.

arXiv comment13 pages. Many diagrams drawn in TikZ. Essentially-final version, to appear in Proceedings of the Conference String-Math 2013. Small changes made between v2 and v3; primarily clarifications