The background field method and the linearization problem for Poisson manifolds

P. A. Grassi; A. Quadri

doi:10.1016/j.nuclphysb.2004.10.046

The background field method and the linearization problem for Poisson manifolds

P. A. Grassi, A. Quadri

Dipartimento di Scienze e Innovazione Tecnologica

Risultato della ricerca: Contributo su rivista › Articolo in rivista › peer review

Abstract

The background field method (BFM) for the Poisson sigma model (PSM) is studied as an example of the application of the BFM technique to open gauge algebras. The relationship with Seiberg-Witten maps arising in non-commutative gauge theories is clarified. It is shown that the implementation of the BFM for the PSM in the Batalin-Vilkovisky formalism is equivalent to the solution of a generalized linearization problem (in the formal sense) for Poisson structures in the presence of gauge fields. Sufficient conditions for the existence of a solution and a constructive method to derive it are presented.

Lingua originale	Inglese
pagine (da-a)	549-568
Numero di pagine	20
Rivista	Nuclear Physics B
Volume	706
Numero di pubblicazione	3
DOI	https://doi.org/10.1016/j.nuclphysb.2004.10.046
Stato di pubblicazione	Pubblicato - 7 feb 2005

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10.1016/j.nuclphysb.2004.10.046

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abstract = "The background field method (BFM) for the Poisson sigma model (PSM) is studied as an example of the application of the BFM technique to open gauge algebras. The relationship with Seiberg-Witten maps arising in non-commutative gauge theories is clarified. It is shown that the implementation of the BFM for the PSM in the Batalin-Vilkovisky formalism is equivalent to the solution of a generalized linearization problem (in the formal sense) for Poisson structures in the presence of gauge fields. Sufficient conditions for the existence of a solution and a constructive method to derive it are presented.",

author = "Grassi, {P. A.} and A. Quadri",

note = "Funding Information: One of us (A.Q.) would like to thank A. Cattaneo for useful discussions. R. Stora and G. Barnich are acknowledged for suggestions and comments. The research of P.A.G. is partially funded by NSF GRANT PHY-0098527 and University of Piemonte Orientale. P.A.G. and A.Q. thank the Theory Division at CERN where this work was started and was completed. ",

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AB - The background field method (BFM) for the Poisson sigma model (PSM) is studied as an example of the application of the BFM technique to open gauge algebras. The relationship with Seiberg-Witten maps arising in non-commutative gauge theories is clarified. It is shown that the implementation of the BFM for the PSM in the Batalin-Vilkovisky formalism is equivalent to the solution of a generalized linearization problem (in the formal sense) for Poisson structures in the presence of gauge fields. Sufficient conditions for the existence of a solution and a constructive method to derive it are presented.

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The background field method and the linearization problem for Poisson manifolds

Abstract

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