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Coisotropic submanifolds and dual pairs


Cattaneo, Alberto S (2014). Coisotropic submanifolds and dual pairs. Letters in Mathematical Physics, 104(3):243-270.

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.

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2014
Deposited On:22 Nov 2013 11:46
Last Modified:05 Apr 2016 17:10
Publisher:Springer
ISSN:0377-9017
Publisher DOI:https://doi.org/10.1007/s11005-013-0661-2
Official URL:http://link.springer.com/article/10.1007%2Fs11005-013-0661-2
Related URLs:http://arxiv.org/abs/1306.3249

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