M theory on `toric' G(2) cones and its type II reduction

We analyze a class of conical G2 metrics admitting two commuting isometries, together with a certain one-parameter family of G2 deformations which preserves these symmetries. Upon using recent results of Calderbank and Pedersen, we extract the IIA reduction of eleven-dimensional supergravity on such backgrounds, as well as its type IIB dual. The associated type II solutions are expected to contain 6-branes and 5-branes respectively. By studying the general asympotics of the IIA and IIB solutions around the relevant loci, we confirm the interpretation of such solutions in terms of localized and delocalized branes. In particular, we find explicit, general expressions for the string coupling and R-R/NS-NS fields in the vicinity of these objects. Our solutions contain and generalize the field configurations relevant for certain models considered in recent work of Acharya and Witten.