The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction

Details The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction The Hitchin Model, Poisson-quasi-Nijenhuis Geometry and Symmetry Reduction

2007-06-09

arxiv.org/abs/0706.1289v2

JHEP 0710:075,2007

Physics

High Energy Physics

High Energy Physics - Theory

38 pages, no figures, LaTex. One paragraph in sect. 6 and 3 references added

Scientific paper

10.1088/1126-6708/2007/10/075

We revisit our earlier work on the AKSZ formulation of topological sigma model on generalized complex manifolds, or Hitchin model. We show that the target space geometry geometry implied by the BV master equations is Poisson--quasi--Nijenhuis geometry recently introduced and studied by Sti\'enon and Xu (in the untwisted case). Poisson--quasi--Nijenhuis geometry is more general than generalized complex geometry and comprises it as a particular case. Next, we show how gauging and reduction can be implemented in the Hitchin model. We find that the geometry resulting form the BV master equation is closely related to but more general than that recently described by Lin and Tolman, suggesting a natural framework for the study of reduction of Poisson--quasi--Nijenhuis manifolds.

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