Dimensional reduction of Courant sigma models and Lie theory of Poisson groupoids

Groupoids and Poisson Sigma Models with Boundary

This note gives an overview on the construction of symplectic groupoids as reduced phase spaces of Poisson sigma models and its generalization in the infinite dimensional setting (before reduction).

Poisson Sigma Models and Symplectic Groupoids

We consider the Poisson sigma model associated to a Poisson manifold. The perturbative quantization of this model yields the Kontsevich star product formula. We study here the classical model in the Hamiltonian formalism. The phase space is the space of leaves of a Hamiltonian foliation and has a natural groupoid structure. If it is a manifold then it is a symplectic groupoid for the given Pois...

Lie, symplectic and Poisson groupoids and their Lie algebroids

Poisson–Lie T–plurality of three–dimensional conformally invariant sigma models

Starting from the classification of 6–dimensional real Drinfeld doubles and their decomposition into Manin triples we construct 3–dimensional Poisson–Lie T–dual or more precisely T–plural sigma models. Of special interest are those that are conformally invariant. Examples of models that satisfy vanishing β–function equations with zero dilaton are presented and their duals are calculated. It tur...

Lie - Poisson spaces and reduction

The category of Banach Lie-Poisson spaces is introduced and studied. It is shown that the category of W ∗-algebras can be considered as one of its subcategories. Examples and applications of Banach Lie-Poisson spaces to quantization and integration of Hamiltonian systems are also given.