Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model
By Alberto S. Cattaneo, Giovanni Felder. 2003
142 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f51ad5ad412708c3dae413bdda4c29a8ce6243f3
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In Algebra and Number Theory
- Damien Calaque
- Michel van den Bergh
- R. Szabo
- Osamu Iyama
- Tatiana Gateva-Ivanova
- Raf Bocklandt
- Nathan Broomhead
- Lingyan Guo
In Geometry and Topology
- Michel van den Bergh
- R. Szabo
- Damien Calaque
- Yukinobu Toda
- Osamu Iyama
- Tatiana Gateva-Ivanova
- Markus Reineke
- Raf Bocklandt
In Mathematical Physics
- Damien Calaque
- Michel van den Bergh
- R. Szabo
- Yukinobu Toda
- Markus Reineke
- Daisuke Yamakawa
- Osamu Iyama
- Dmitri Orlov
Citations in the corpus
- Lectures on integrability of Lie brackets (2006, unknown): “The problem of integrating coisotropic submanifolds was solved by Cattaneo and Felder in [9].”
- Hochschild cohomology and Atiyah classes (2007, methodology): “As explained to us by Torossian this can be obtained from the work of Cattaneo and Felder on the quantization of coisotropic submanifolds [9, 10].”
- Symmetry, gravity and noncommutativity (2006, background): “le of D-branes for the open topological A-model string theory (called A-branes for short). In this case the quantization can be related to the deformation quantization in the induced Poisson brackets [31, 32], as we now describe explicitly. Branes defined by second-class constraints may also be treat”