A search for AdS₅ × S² IIB supergravity solutions dual to N = 2 SCFTs

We present a systematic search for Type IIB supergravity solutions whose spacetimes include AdS₅ and S² factors, which would be candidate duals to N = 2 fourdimensional Superconformal field theories. The candidate solutions encode the SU(2) Rsymmetry geometrically on the S ² and an additional Killing vector generates the U(1) R-symmetry. By analysing the Killing spinor equations we show that no such solutions exist. This suggests that if Type IIB backgrounds dual to N = 2 SCFTs exist, the SU(2) R-symmetry is realised non-geometrically. Finally, we also show that, in the context of both N = 1 and N = 2 Type IIB backgrounds with an AdS5 factor, the only candidate U(1) R-symmetry Killing vector directions are the ones that appear for generic values of the Killing spinors; no further Killing vectors exist for special values of the Killing spinors.