Consistent Type IIB Reductions to Maximal 5D Supergravity

TL;DR

The paper develops explicit, non-linear reduction formulas for Type IIB supergravity on $AdS_5\times S^5$ and its non-compact analogues, using ${\rm E}_{6(6)}$ exceptional field theory to realize generalized Scherk-Schwarz reductions. It shows that these reductions produce maximal $D=5$ gauged supergravities with gauge groups ${\rm SO}(p,q)$ and that every $D=5$ solution uplifts to a Type IIB solution, ensuring consistency for stationary points and holographic RG flows. The authors provide complete uplift formulas for all IIB fields, including a thorough reconstruction of the self-dual 4-form, and analyze the background geometries that correspond to the known AdS$_5\times S^5$ and dS$_5\times H^{3,3}$ vacua. The work thereby furnishes a robust, covariant framework for embedding 5D gauged supergravities into IIB, with broad potential applications to holography and consistent truncations.

Abstract

We use exceptional field theory as a tool to work out the full non-linear reduction ansaetze for the AdS$_5\times S^5$ compactification of IIB supergravity and its non-compact counterparts in which the sphere $S^5$ is replaced by the inhomogeneous hyperboloidal space $H^{p,q}$. The resulting theories are the maximal 5D supergravities with gauge groups SO(p,q). They are consistent truncations in the sense that every solution of 5D supergravity lifts to a solution of IIB supergravity. In particular, every stationary point and every holographic RG flow of the scalar potentials for the compact and non-compact 5D gaugings directly lift to solutions of IIB supergravity.