Star products and branes in Poisson-Sigma models

TL;DR

This paper demonstrates that non-coisotropic branes in Poisson-Sigma models can be quantized at the quantum level, leading to the Kontsevich star product for Dirac brackets, and discusses mixed constraint cases.

Contribution

It extends the quantization framework of Poisson-Sigma models to include non-coisotropic branes and mixed constraints, connecting to Kontsevich's star product.

Findings

Quantum non-coisotropic branes are consistent in Poisson-Sigma models.

Quantization yields Kontsevich's star product for Dirac brackets.

Analysis includes cases with both first and second-class constraints.

Abstract

We prove that non-coisotropic branes in the Poisson-Sigma model are allowed at the quantum level. When the brane is defined by second-class constraints, the perturbative quantization of the model yields the Kontsevich's star product associated to the Dirac bracket on the brane. We also discuss the quantization when both first and second-class constraints are present.