Almost Contact Metric Structures of M-Theory Dual of Large-N Thermal QCD-Like Theories

Abstract

The study of gravity dual of large-N gauge theories via AdS/CFT correspondence have been very successful in the understanding of both quantum gravity and strongly coupled field theories. The dual gravitational theory in these cases is usually a weakly coupled type IIB string theory in AdS5 × S5 background which under the considerations of low energy can be adequately explained via type IIB supergravity. However the gauge theories considered are generally supersymmetric and conformal, therefore not realistic. Breaking of supersymmetry and the conformal symmetry has previously been considered in the literature via the use of conifold geometries in place of S5 and via fractional D3-branes respectively. But these solutions still lacked UV conformality and fundamental quarks. A complete setup was only obtained recently with the use of Ouyang embedding and anti D-branes on a wrapped resolved deformed conifold. Furthermore, its local M-theory uplift has also been constructed which made it possible to study the gravity dual at finite coupling. This construction has prompted a need to understand the underlying internal geometries of the dual M-theory uplift, where the presence of a seven dimensional G2 manifold has been established which is revisited in this work. On the other hand in recent literature the use of almost contact structures is becoming prominent in the study of such manifolds with G2 structure group. The need for establishing almost contact structure in an odd dimensional manifold can be as important as the need for almost complex structure in a complex manifold like the Calabi-Yau. Thus in this work we review these structures in the case of the dual M-theory uplift and verify the related calculations that are presented in [1] which helped in the better understanding of the associated transverse geometry of the G2 internal manifold. We conclude in agreement to [1] that there exist an contact 3-structure under general situations.