Supersymmetric configurations, geometric transitions and new non-Kähler manifolds

We give a detailed derivation of a supersymmetric configuration of wrapped D5 branes on a two-cycle of a warped resolved conifold. Our analysis reveals that the resolved conifold should support a non-Kähler metric with an SU(3) structure. We use this as a starting point of the geometric transition in type IIB theory. A mirror, and a subsequent flop transition using an intermediate M-theory configuration with a G₂ structure, gives rise to the complete IR geometric transition in type IIA theory. A further mirror transformation gives the type IIB gravity dual of the IR gauge theory on the wrapped D5 branes. Expectedly non-Kähler deformations of the resolved and the deformed conifolds appear as the gravity duals of the confining gauge theories in type IIA and type IIB theories respectively, although in more generic cases these manifolds could also be non-geometric. In the local limit we reproduce precisely the scenarios presented in our earlier works. Our present work should therefore be viewed as providing a supergravity proof of geometric transitions in the full global scenarios in type II theories.