Three Dimensional Topological Field Theory induced from Generalized Complex Structure

Details Three Dimensional Topological Field Theory induced from Generalized Complex Structure Three Dimensional Topological Field Theory induced from Generalized Complex Structure

2004-12-14

arxiv.org/abs/hep-th/0412140v2

Int.J.Mod.Phys.A22:4679-4694,2007

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

10.1142/S0217751X07037196

We construct a three-dimensional topological sigma model which is induced from a generalized complex structure on a target generalized complex manifold. This model is constructed from maps from a three-dimensional manifold $X$ to an arbitrary generalized complex manifold $M$. The theory is invariant under the diffeomorphism on the world volume and the $b$-transformation on the generalized complex structure. Moreover the model is manifestly invariant under the mirror symmetry. We derive from this model the Zucchini's two dimensional topological sigma model with a generalized complex structure as a boundary action on $\partial X$. As a special case, we obtain three dimensional realization of a WZ-Poisson manifold.

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