ar X iv : h ep - t h / 06 03 01 6 v 2 9 M ay 2 00 6 hep - th / 0603016 ITFA - 2006 - 04 Kaluza - Klein Holography

We construct a holographic map between asymptotically AdS5 × S5 solutions of 10d supergravity and vacuum expectation values of gauge invariant operators of the dual QFT. The ingredients that enter in the construction are (i) gauge invariant variables so that the KK reduction is independent of any choice of gauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions (constructed perturbatively in the number of fields); (iii) application of holographic renormalization. A non-trivial role in the last step is played by extremal couplings. This map allows one to reliably compute vevs of operators dual to any KK fields. As an application we consider a Coulomb branch solution and compute the first two non-trivial vevs, involving operators of dimension 2 and 4, and reproduce the field theory result, in agreement with non-renormalization theorems. This constitutes the first quantitative test of the gravity/gauge theory duality away from the conformal point involving a vev of an operator dual to a KK field (which is not one of the gauged supergravity fields).