Abstract
We first give a proof that the supersymmetric configurations satisfy the equations of motion for type II supergravity. In flux compactifications, the string vacua preserving N = 2 supersymmetry are the twisted generalized Calabi–Yau manifold. The modulus space of the string vacua can be constructed. We discuss the generalized Dirac operator which adds a torsional term to the ordinary Dirac operator and compute its index by the path integral method. Via the variation of the action of supergravity one can introduce the generalized Ricci flow equations. We consider deforming the manifold with the generalized Ricci flow. Finally, we consider the linear stability of the fixed points of the generalized Ricci flow.
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