An eight-dimensional approach to G2 manifolds

We develop a systematic approach to G2 holonomy manifolds with an SU(2)×SU(2) isometry using maximal eight-dimensional gauged supergravity to describe D6-branes wrapped on deformed three-spheres. A quite general metric ansatz that generalizes the celebrated Bryant–Salamon metric involves nine functions. We show that only six of them are the independent ones and derive the general first order system of differential equations that they obey. As a byproduct of our analysis, we generalize the notion of the twist that relates the spin and gauge connections in a way that involves non-trivially the scalar fields.