Coisotropic Submanifolds and Dual Pairs

The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropic submanifolds (a result announced in [math.QA/0309180]) and that the corresponding reduced phase space is a (possibly singular) dual pair between the reduced spaces of the given two coisotropic submanifolds. In addition the generalization to a more general tensor field is considered and it is shown that the theory produces Lagrangian evolution relations if and only if the tensor field is Poisson. DOI: https://doi.org/10.1007/s11005-013-0661-2 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi.org/10.5167/uzh-85296 Originally published at: Cattaneo, Alberto S (2014). Coisotropic submanifolds and dual pairs. Letters in Mathematical Physics, 104(3):243-270. DOI: https://doi.org/10.1007/s11005-013-0661-2 DOI 10.1007/s11005-013-0661-2 Lett Math Phys Coisotropic Submanifolds and Dual Pairs ALBERTO S. CATTANEO Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057 Zurich, Switzerland. e-mail: [email protected] Received: 22 June 2013 / Revised: 11 October 2013 / Accepted: 12 October 2013 © Springer Science+Business Media Dordrecht 2013 Abstract. The Poisson sigma model is a widely studied two-dimensional topological field theory. This note shows that boundary conditions for the Poisson sigma model are related to coisotropic submanifolds (a result announced in [math.QA/0309180]) and that the corresponding reduced phase space is a (possibly singular) dual pair between the reduced spaces of the given two coisotropic submanifolds. In addition the generalization to a more general tensor field is considered and it is shown that the theory produces Lagrangian evolution relations if and only if the tensor field is Poisson. Mathematics Subject Classification (1991). Primary 53D17; Secondary 81T45, 53D20, 58H05.