Type IIB solutions with interpolating supersymmetries

We study type IIB supergravity solutions with four supersymmetries that interpolate between two types widely considered in the literature: the dual of the Becker-Becker compactifications of M theory to three dimensions and the dual of Strominger’s torsion compactifications of heterotic theory to four dimensions. We find that for all intermediate solutions the internal manifold is not Calabi-Yau type, but has an $\mathrm{SU}\left(3\right)\mathrm{}$ holonomy in connection with a torsion given by the 3-form flux. All 3-form and 5-form fluxes, as well as the dilaton, depend on one function appearing in the supersymmetry spinor, which satisfies a nonlinear differential equation. We check that the fields corresponding to a flat bound state of D3- and D5-branes lie in our class of solutions. The relations among supergravity fields that we derive should be useful in studying new gravity duals of gauge theories, as well as possibly compactifications.