5 Poisson - Dirac branes in Poisson - Sigma models by Iván Calvo and Fernando Falceto

Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras

We continue the study of the Poisson-Sigma model over Poisson-Lie groups. Firstly, we solve the models with targets G and G∗ (the dual group of the Poisson-Lie group G) corresponding to a triangular r-matrix and show that the model over G∗ is always equivalent to BF-theory. Then, given an arbitrary r-matrix, we address the problem of finding D-branes preserving the duality between the models. W...

Star products and branes in Poisson-Sigma models

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 Kontsevich’s star product associated to the Dirac bracket on the brane. Finally, we present the quantization for a general brane.

Coisotropic embeddings in Poisson manifolds

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition, already considered by Calvo and Falceto (2004), sits coisotropically inside some larger cosymplectic submanifold, wh...

Reduction of Dirac structures along isotropic subbundles

Given a Dirac subbundle and an isotropic subbundle, we provide a canonical method to obtain a new Dirac subbundle. When the original Dirac subbundle is Courant involutive this construction has interesting applications, unifying and generalizing some results on the reduction of Dirac structures previously found in the literature.

Poisson Sigma Models on Surfaces with Boundary: Classical and Quantum Aspects