Topological strings in generalized complex space

TL;DR

This paper constructs a two-dimensional topological sigma-model on generalized Calabi-Yau spaces using generalized complex structures and pure spinors, revealing new insights into moduli spaces and noncommutative products.

Contribution

It introduces a novel topological sigma-model framework based on generalized complex geometry, with off-shell closure and explicit links to noncommutative deformation theory.

Findings

Model depends only on generalized complex structure J

Off-shell closure of Q-transformations achieved

Connection to holomorphic noncommutative Kontsevich *-product

Abstract

A two-dimensional topological sigma-model on a generalized Calabi-Yau target space $X$ is defined. The model is constructed in Batalin-Vilkovisky formalism using only a generalized complex structure $J$ and a pure spinor $\rho$ on $X$. In the present construction the algebra of $Q$-transformations automatically closes off-shell, the model transparently depends only on $J$, 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 N=2 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 $\beta$ and recover holomorphic noncommutative Kontsevich $*$-product.