Supersymmetric AdS5 solutions of type IIB supergravity without D3 branes

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, where the five-form flux vanishes, while all remaining fluxes are allowed to be non-vanishing consistent with SO(4,2) symmetry. This completes the program of classifying all supersymmetric solutions of ten and eleven-dimensional supergravity with an AdS(5) factor. We investigate the supersymmetry conditions in some special cases, and demonstrate how these are satisfied by a solution originally found in [13], utilising the method of non-Abelian T-duality.