Abstract:

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-Kahler 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-Kahler
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.