Monday, June 17, 2013

1306.3249 (Alberto S. Cattaneo)

Coisotropic submanifolds and dual pairs    [PDF]

Alberto S. Cattaneo
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 in one-to-one correspondence with 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.
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