D = 5 SU(2) × U(1) gauged supergravity from D = 11 supergravity

Abstract

We consider the most general class of supersymmetric solutions of D = 11 supergravity consisting of a warped product of AdS 5 with a six-dimensional internal manifold 6, which are dual to N = 2 super conformal field theories in d = 4. For any such 6 we construct the full non-linear Kaluza-Klein ansatz for the reduction of D = 11 supergravity on 6 down to D = 5 SU(2) × U(1) gauged supergravity, at the level of the bosonic fields. This allows one to uplift any solution of the D = 5 supergravity to obtain a solution of D = 11 supergravity for any given 6. Using an explicit 6, corresponding to M5-branes wrapping holomorphic curves in a Calabi-Yau two-fold, we uplift some solutions and comment upon their interpretation.