Consistent Kaluza-Klein Reductions for General Supersymmetric AdS Solutions

TL;DR

This work constructs explicit, bosonic consistent Kaluza-Klein reductions for the most general $AdS_5\times_w M_5$ solutions in type IIB (on $M_5$) and for general $AdS_4$ configurations in $D=11$ (including $AdS_4\times SE_7$ and SLAG-3 flux geometries) to minimal gauged supergravity in $D=5$ and $D=4$, respectively. By formulating detailed reduction ansätze and verifying the supersymmetry variations, the authors demonstrate that any solution of the lower-dimensional gauged supergravity uplifts to a full ten- or eleven-dimensional solution, with precise matching of the bosonic equations $R_{ ho\sigma}$ and $F$-field dynamics and the fermionic SUSY variations. The results provide concrete evidence for a broader conjecture that warped AdS solutions admit consistent truncations to gauged supergravities, encapsulating the current multiplets of the dual SCFTs and enabling systematic uplifts of holographic solutions. The methods rely on G-structure bilinears on the internal manifolds and yield explicit, gauge-field–coupled ansätze that preserve supersymmetry in the uplift.

Abstract

For the most general supersymmetric solutions of type IIB supergravity consisting of a warped product of AdS_5 with a five-dimensional manifold M_5, we construct an explicit consistent Kaluza-Klein reduction on M_5 to minimal D=5 gauged supergravity. Thus, any solution of the gauged supergravity can be uplifted on M_5 to obtain an exact solution of type IIB supergravity. We also show that for general AdS_4 x SE_7 solutions, where SE_7 is a seven-dimensional Sasaki-Einstein manifold, and for a general class of supersymmetric solutions that are a warped product of AdS_4 with a seven-dimensional manifold N_7, there is an analogous consistent reduction to minimal D=4 gauged supergravity.