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

Abstract

We show that the 2d Poisson Sigma Model on a Poisson groupoid arises as an effective theory of the 3d Courant Sigma Model associated to the double of the underlying Lie bialgebroid. This field-theoretic result follows from a Lie-theoretic one involving a coisotropic reduction of the odd cotangent bundle by a generalized space of algebroid paths. We also provide several examples, including the case of symplectic groupoids in which we relate the symplectic realization construction of Crainic-Marcut to a particular gauge fixing of the 3d theory.

arXiv comment37 pages

References in corpus (21)

• The Geometry of the Master Equation and Topological Quantum Field Theory
• A path integral approach to the Kontsevich quantization formula
• Geometry of Batalin-Vilkovisky quantization
• Topological boundary conditions in abelian Chern-Simons theory
• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• WZW-Poisson manifolds
• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Higher vector bundles and multi-graded symplectic manifolds
• Classical BV theories on manifolds with boundary
• Poisson sigma models and symplectic groupoids
• Introduction to supergeometry
• The Topological G/G WZW Model in the Generalized Momentum Representation
• On the integration of Poisson manifolds, Lie algebroids, and coisotropic submanifolds
• Poisson-Lie T-duality as a boundary phenomenon of Chern-Simons theory
• Topological Poisson Sigma models on Poisson-Lie groups
• On local integration of Lie brackets
• Towards holography in the BV-BFV setting
• Poisson sigma model over group manifolds
• Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
• Renormalization group flow of Chern-Simons boundary conditions and generalized Ricci tensor
• On Nonlinear Gauge Theories