Supersymmetric Configurations, Geometric Transitions and New Non-Kahler Manifolds

TL;DR

This paper derives supersymmetric configurations of wrapped D5-branes on a warped resolved conifold, revealing non-Kahler geometries with SU(3) structure and demonstrating geometric transitions in type II string theories with gravity duals of confining gauge theories.

Contribution

It provides a supergravity derivation of geometric transitions involving non-Kahler manifolds with SU(3) structure in full global scenarios of type II string theories.

Findings

Resolved conifold supports a non-Kahler SU(3) structure.

Geometric transitions relate type IIB and type IIA theories via mirror and flop transitions.

Gravity duals of confining gauge theories involve non-Kahler deformations of conifolds.

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 G_2 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.