New G2 holonomy metrics, D6 branes with inherent

New G 2 holonomy metrics, D6 branes with inherent U (1) × U (1) isometry and γ-deformations Abstract It is found the most general local form of the 11-dimensional supergravity backgrounds which, by reduction along one isometry, give rise to IIA supergravity solutions with a RR field and a non trivial dilaton, and for which the condition F (1,1) = 0 holds. This condition is stronger than the usual condition F ab J ab = 0, required by supersymmetry. It is shown that these D6 wrapped backgrounds arise from the direct sum of the flat Minkowski metric with certain G 2 holonomy metrics admitting an U (1) action, with a local form found by Apostolov and Salamon. Indeed, the strong supersymmetry condition is equivalent to the statement that there is a new isometry on the G 2 manifold, which commutes with the old one; therefore these metrics are inherently toric. An example that is asymptotically Calabi-Yau is presented. There are found another G 2 metrics which give rise to half-flat SU (3) structures. All this examples possess an U (1) × U (1) × U (1) isometry subgroup. Supergravity solutions without fluxes corresponding to these G 2 metrics are constructed. The presence of a T 3 subgroup of isometries permits to apply the γ-deformation technique in order to generate new supergravity solutions with fluxes.