1307.5812 (Theo Johnson-Freyd)

Poisson AKSZ theories and their quantizations    [PDF]

Theo Johnson-Freyd

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. As an example, the one-dimensional AKSZ construction has a canonical quantization, giving a canonical $\star$-quantization of Poisson formal manifolds.

View original: http://arxiv.org/abs/1307.5812