Poisson-Dirac branes in Poisson-Sigma models

TL;DR

This paper investigates boundary conditions in Poisson-sigma models, explores their phase space structure, and connects perturbative quantization with Kontsevich's deformation quantization formula for Dirac brackets.

Contribution

It introduces a comprehensive analysis of boundary conditions (branes) in Poisson-sigma models and links their quantization to Kontsevich's deformation quantization.

Findings

Characterization of boundary conditions compatible with Poisson-sigma models

Analysis of phase space structure on the strip with these boundary conditions

Perturbative quantization on the disc relates to Kontsevich's deformation formula

Abstract

We analyse the general boundary conditions (branes) consistent with the Poisson-sigma model and study the structure of the phase space of the model defined on the strip with these boundary conditions. Finally, we discuss the perturbative quantization of the model on the disc with a Poisson-Dirac brane and relate it to Kontsevich's formula for the deformation quantization of the Dirac bracket induced on the brane.