New compactifications of supergravities and large-N QCD

We construct supergravity backgrounds representing non-homogeneous compactifications of d = 10, 11 supergravities to four dimensions, which cannot be written as a direct product. The geometries are regular and approach AdS7 x S4 or AdS5 x S5 at infinity; they are generically nonsupersymmetric, except in a certain 'extremal' limit, where a Bogomol'nyi bound is saturated and a naked singularity appears. By using these spaces, one can construct a model of QCD that generalizes by one (or two) extra parameters a recently proposed model of QCD based on the non-extremal D4-brane. This allows for some extra freedom to circumvent some (but not all) limitations of the simplest version