Generalized structures of 풩 = 1 vacua.

We characterize 풩 = 1 vacua of type-II theories in terms of generalized complex structure on the internal manifold M. The structure group of T(M)⊕T*(M) being SU(3) × SU(3) implies the existence of two pure spinors Φ₁ and Φ₂. The conditions for preserving 풩 = 1 supersymmetry turn out to be simple generalizations of equations that have appeared in the context of 풩 = 2 and topological strings. They are (d+H∧)Φ₁ = 0 and (d+H∧)Φ₂ = F_RR. The equation for the first pure spinor implies that the internal space is a twisted generalized Calabi-Yau manifold of a hybrid complex-symplectic type, while the RR-fields serve as an integrability defect for the second. [ABSTRACT FROM AUTHOR]