Kaluza-Klein Holography
Kostas Skenderis, Marika Taylor
TL;DR
The paper develops a complete holographic map between asymptotically AdS5 × S5 solutions in IIB supergravity and vevs of dual gauge-invariant operators, using a gauge-invariant non-linear KK reduction together with holographic renormalization and careful treatment of extremal couplings. It shows how to extract vevs for operators dual to any KK field from the 10D to 5D reduction, and validates the approach by a Coulomb-branch test in N=4 SYM where the first non-trivial vevs (dimensions 2 and 4) precisely match field theory. The method provides a principled framework to read off 1-point functions from full KK spectra, beyond the gauged supergravity sector, and to reconstruct bulk geometry from boundary data via the radial Hamiltonian formalism. This constitutes the first quantitative non-conformal test of gravity/gauge duality involving a vev of a KK-dual operator and offers a general algorithm for holographic vevs in AdS/CFT setups with KK modes.
Abstract
We construct a holographic map between asymptotically AdS_5 x S^5 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).