Poisson reduction and branes in Poisson-Sigma models

TL;DR

This paper investigates boundary conditions in Poisson-Sigma models, extending the types of allowed branes and relating the phase space to generalized Dirac brackets through Poisson reduction.

Contribution

It introduces the concept of non-coisotropic branes and connects the phase space to generalized Dirac brackets via Poisson reduction.

Findings

Non-coisotropic branes are permissible boundary conditions.

The phase space relates to generalized Dirac brackets.

Poisson reduction leads to a broader class of Poisson algebras.

Abstract

We analyse the problem of boundary conditions for the Poisson-Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a Poisson algebra that generalizes Dirac's construction. The phase space of the model on the strip is related to the (generalized) Dirac bracket on the branes through a dual pair structure.