Topological strings in generalized complex space

Abstract

A two-dimensional topological sigma-model on a generalized CalabiYau target space X is defined. The model is constructed in a Batalin-Vilkovisky formalism using only a generalized complex structure script T and a pure spinor ρ on X. In the present construction, the algebra of Q-transformations automatically closes off-shell, the model transparently depends only on script T, the algebra of observables and correlation functions for topologically trivial maps in genus zero are easily defined. The extended moduli space appears naturally. The familiar action of the twisted script N = 2 conformai field theory (CFT) can be recovered after a gauge fixing. In the open case, we consider an example of generalized deformation of complex structure by a holomorphic Poisson bivector β and recover holomorphic noncommutative Kontsevich *-product. © 2007 International Press.