Supersymmetric AdS_5 Solutions of Type IIB Supergravity

TL;DR

This work determines the necessary and sufficient conditions for supersymmetric Type IIB backgrounds with an $AdS_5$ factor, by encoding the geometry of the internal manifold $M_5$ in a local identity $G$-structure. The authors show that a Killing vector $K_5$ emerges and SUSY constrains the fluxes $(P,G,F)$ and warp factor $Δ$ so that the full equations of motion are implied by supersymmetry. In a tractable subcase with constant dilaton and vanishing axion, the problem reduces to a second-order nonlinear ODE whose analytic PW solution is recovered and whose numerical solutions suggest a broader local family, though global consistency (spinor and flux definability) remains problematic. The results provide a robust framework for constructing explicit $AdS_5$ backgrounds dual to 4D SCFTs beyond Sasaki–Einstein geometries and point to future work on global topology and exact solutions.

Abstract

We analyse the most general bosonic supersymmetric solutions of type IIB supergravity whose metrics are warped products of five-dimensional anti-de Sitter space AdS_5 with a five-dimensional Riemannian manifold M_5. All fluxes are allowed to be non-vanishing consistent with SO(4,2) symmetry. We show that the necessary and sufficient conditions can be phrased in terms of a local identity structure on M_5. For a special class, with constant dilaton and vanishing axion, we reduce the problem to solving a second order non-linear ODE. We find an exact solution of the ODE which reproduces a solution first found by Pilch and Warner. A numerical analysis of the ODE reveals an additional class of local solutions.