Topological twisted sigma model with H-flux revisited

In this paper we revisit the topological twisted sigma model with H-flux. We explicitly expand and then twist the worldsheet Lagrangian for bi-Hermitian geometry. we show that the resulting action consists of a BRST exact term and pullback terms, which only depend on one of the two generalized complex structures and the B-field. We then discuss the topological feature of the model.