The background field method and the linearization problem for Poisson manifolds

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.

Generalized complex geometry, generalized branes and the Hitchin sigma model

“…sect. 4) following the original work of Cattaneo and Felder in [35] (see also [45][46][47]). We shall limit ourselves to the lowest order in perturbation theory, since the constraints on target space geometry following from the Batalin-Vilkovisky classical master equation lead directly to Hitchin's generalized complex geometry.…”