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

TL;DR

This work addresses whether Type IIB supergravity admits $AdS_5\times S^2$ backgrounds that realize the full ${\cal N}=2$ superconformal symmetry via a geometric $SU(2)$ R-symmetry on $S^2$ and a $U(1)$ R-symmetry from a Killing vector. Using a rigorous Killing spinor equation analysis with a three-dimensional spinor-bilinear framework, the authors show that no nontrivial solutions exist beyond the familiar $AdS_5\times S^5$ background; in particular, the $SU(2)$ R-symmetry cannot be realized geometrically in this setting. They also establish that for ${\cal N}=1$ or ${\cal N}=2$ AdS$_5$ backgrounds the only candidate $U(1)$ R-symmetry directions arise from generic spinor configurations, with no extra Killing vectors for special spinor values. The results strongly suggest that any Type IIB duals to ${\cal N}=2$ SCFTs would require a non-geometric realization of the $SU(2)$ R-symmetry, refining the search for holographic ${\cal N}=2$ vacua in IIB string theory.

Abstract

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 four-dimensional Superconformal field theories. The candidate solutions encode the SU(2) R-symmetry geometrically on the S2 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.