Kaluza-Klein holography

We construct a holographic map between asymptotically AdS_5 x S^5 solutionsof 10d supergravity and vacuum expectation values of gauge invariant operatorsof the dual QFT. The ingredients that enter in the construction are (i) gaugeinvariant variables so that the KK reduction is independent of any choice ofgauge fixing; (ii) the non-linear KK reduction map from 10 to 5 dimensions(constructed perturbatively in the number of fields); (iii) application ofholographic renormalization. A non-trivial role in the last step is played byextremal couplings. This map allows one to reliably compute vevs of operatorsdual to any KK fields. As an application we consider a Coulomb branch solutionand compute the first two non-trivial vevs, involving operators of dimension 2and 4, and reproduce the field theory result, in agreement withnon-renormalization theorems. This constitutes the first quantitative test ofthe gravity/gauge theory duality away from the conformal point involving a vevof an operator dual to a KK field (which is not one of the gauged supergravityfields).Comment: 47 pages, v2: minor improvements, version to appear in JHE