Geometric quantization and non-perturbative Poisson sigma model

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dc.creatorBonechi, Francesco
dc.creatorCattaneo, Alberto S.
dc.creatorZabzine, Maxim
dc.date2005-07-11
dc.date2006-08-11
dc.date.accessioned2026-07-07T07:37:45Z
dc.date.available2026-07-07T07:37:45Z
dc.descriptionIn this note we point out the striking relation between the conditions arising within geometric quantization and the non-perturbative Poisson sigma model. Starting from the Poisson sigma model, we analyze necessary requirements on the path integral measure which imply a certain integrality condition for the Poisson cohomology class $[α]$. The same condition was considered before by Crainic and Zhu but in a different context. In the case when $[α]$ is in the image of the sharp map we reproduce the Vaisman's condition for prequantizable Poisson manifolds. For integrable Poisson manifolds we show, with a different procedure than in Crainic and Zhu, that our integrality condition implies the prequantizability of the symplectic groupoid. Using the relation between prequantization and symplectic reduction we construct the explicit prequantum line bundle for a symplectic groupoid. This picture supports the program of quantization of Poisson manifold via symplectic groupoid. At the end we discuss the case of a generic coisotropic D-brane.
dc.description29 pages
dc.identifierhttps://arxiv.org/abs/math/0507223
dc.identifierhttp://arxiv.org/abs/math/0507223
dc.identifierAdv.Theor.Math.Phys.10:683-712,2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120883
dc.subjectSymplectic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleGeometric quantization and non-perturbative Poisson sigma model
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