Consistent type IIB reductions to maximal 5D supergravity

We use exceptional field theory as a tool to work out the full nonlinear reduction ansatz for the AdS₅×S⁵ compactification of IIB supergravity and its noncompact counterparts in which the sphere S⁵ is replaced by the inhomogeneous hyperboloidal space Hp,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 renormalization group flow of the scalar potentials for the compact and noncompact 5D gaugings directly lift to solutions of IIB supergravity.