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Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model


Cattaneo, A S; Felder, G (2004). Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model. Letters in Mathematical Physics, 69:157-175.

Abstract

General boundary conditions (branes'') for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization.

Abstract

General boundary conditions (branes'') for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morphisms and at the perturbative quantum level to the category of associative algebras (deforming algebras of functions on Poisson manifolds) with bimodules as morphisms. Possibly singular Poisson manifolds arising from reduction enter naturally into the picture and, in particular, the construction yields (under certain assumptions) their deformation quantization.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Uncontrolled Keywords:deformation quantization - dual pairs - coisotropic submanifolds - branes
Language:English
Date:2004
Deposited On:27 Jan 2010 12:34
Last Modified:21 Nov 2017 14:21
Publisher:Springer
ISSN:0377-9017
Additional Information:The originalThe original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s11005-004-0609-7

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