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Poisson Reduction and Branes in Poisson–Sigma Models

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Abstract

We analyse the problem of boundary conditions for the Poisson–Sigma model and extend previous results showing that non-coisotropic branes are allowed. We discuss the canonical reduction of a Poisson structure to a submanifold, leading to a Poisson algebra that generalizes Dirac’s construction. The phase space of the model on the strip is related to the (generalized) Dirac bracket on the branes through a dual pair structure.

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References

  • Bojowald M., Strobl T. Classical solutions for Poisson–Sigma models on a Riemman surface, arXiv:hep-th/0304252

  • Bonechi, F. and Zabzine, M.: Poisson–sigma model over group manifolds, arXiv: hep-th/0311213

  • I. Calvo F. Falceto D. García-Álvarez (2003) ArticleTitleTopological Poisson–Sigma models on Poisson–Lie groups JHEP 10 033

    Google Scholar 

  • A.S. Cattaneo G. Felder (2000) ArticleTitleA path integral approach to the Kontsevich quantization formula Commun. Math. Phys. 212 591–611 Occurrence Handle10.1007/s002200000229

    Article  Google Scholar 

  • Cattaneo, A. S. and Felder G.: Coisotropic submanifolds in Poisson geometry and branes in the Poisson sigma model, arXiv:math.QA/0309180.

  • A.S. Cattaneo G. Felder (2001) ArticleTitlePoisson–Sigma models and deformation quantization Mod. Phys. Lett. A 16 179–190

    Google Scholar 

  • Crainic, M. and Fernandes, R. L.: Integrability of Poisson brackets, arXiv:math. DG/0210152

  • F. Falceto K. Gawedzki (2002) ArticleTitleBoundary G/G Theory and topological Poisson–Lie Sigma Model Lett. Math. Phys. 59 61–79

    Google Scholar 

  • M. Hennaux C. Teitelboim (1992) Quantization of Gauge Systems Princeton University Press New Jersey

    Google Scholar 

  • N. Ikeda (1994) ArticleTitleTwo-dimensional gravity and nonlinear gauge theory Ann. Phys. 235 435–464 Occurrence Handle10.1006/aphy.1994.1104

    Article  Google Scholar 

  • T. Kimura (1993) ArticleTitleGeneralized classical BRST cohomology and reduction of Poisson manifolds Commun. Math. Phys. 151 155–182

    Google Scholar 

  • Kontsevich, M.: Deformation quantization of Poisson manifolds, I. IHES M97/72 preprint. arXiv:q-alg/9709040.

  • P. Schaller T. Strobl (1994) ArticleTitlePoisson structure induced (topological) field theories Mod. Phys. Lett. A 9 3129–3136 Occurrence Handle10.1142/S0217732394002951

    Article  Google Scholar 

  • I Vaisman (1994) Lectures on the geometry of Poisson manifolds. Prog. Math Birkhäuser Basel-Boston-Berlin

    Google Scholar 

  • Vaisman, I.: Dirac submanifolds of Jacobi manifolds, arXiv:math.SG/0205019.

  • A. Weinstein (1983) ArticleTitleThe local structure of Poisson manifolds J. Diff. Geom. 18 523–557

    Google Scholar 

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Authors and Affiliations

  1. Depto. Física Teórica, Univ. Zaragoza, E-50009, Zaragoza, Spain

    Iván Calvo & Fernando Falceto

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  1. Iván Calvo
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  2. Fernando Falceto
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Correspondence to Iván Calvo.

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Mathematics Subject Classifications (2000). 81T45, 53D17, 81T30, 53D55.

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Calvo, I., Falceto, F. Poisson Reduction and Branes in Poisson–Sigma Models. Lett Math Phys 70, 231–247 (2004). https://doi.org/10.1007/s11005-004-4302-7

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  • DOI: https://doi.org/10.1007/s11005-004-4302-7

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