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

DOI10.1007/s11005-004-0609-7zbMath1065.53063arXivmath/0309180OpenAlexW3104786246MaRDI QIDQ703995

Giovanni Felder, Alberto Sergio Cattaneo

Publication date: 12 January 2005

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0309180

zbMATH Keywords

quantizationbranescoisotropic submanifolds

Mathematics Subject Classification ID

Quantization in field theory; cohomological methods (81T70) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Poisson manifolds; Poisson groupoids and algebroids (53D17) Momentum maps; symplectic reduction (53D20) Deformation quantization, star products (53D55)

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Cites Work

• The local structure of Poisson manifolds
• Quantum and classical pseudogroups. I: Union pseudogroups and their quantization
• Coisotropic calculus and Poisson groupoids
• Two-dimensional gravity and nonlinear gauge theory
• From local to global deformation quantization of Poisson manifolds
• Remarks on A-branes, mirror symmetry, and the Fukaya category
• Integrability of Lie brackets
• A path integral approach to the Kontsevich quantization formula.
• On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds
• Deformation quantization of Poisson manifolds
• POISSON STRUCTURE INDUCED (TOPOLOGICAL) FIELD THEORIES
• The Geometry of the Master Equation and Topological Quantum Field Theory
• Symplectic groupoids and Poisson manifolds
• On the AKSZ formulation of the Poisson sigma model.
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