Rigidity of SU(2, 2|2)-symmetric solutions in Type IIB

We investigate the existence of half-BPS solutions in Type IIB supergravity which are invariant under the superalgebra SU(2, 2 vertical bar 2) realized on either AdS(5) x S-2 x S-1 or AdS(5) x S-3 warped over a Riemann surface Sigma with boundary. We prove that, in both cases, the only solution is AdS(5) x S-5 itself. We argue that this result provides evidence for the non-existence of fully back-reacted intersecting D3/D7 branes with either AdS(5) x S-2 x S-1 x Sigma or AdS(5) x S-3 x Sigma near-horizon limits.