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

TL;DR

This paper investigates the existence of Type IIB supergravity solutions with AdS5 and S2 factors as duals to N=2 SCFTs, finding no such solutions and suggesting alternative non-geometric realizations of R-symmetry.

Contribution

The study systematically searches for specific supergravity solutions dual to N=2 SCFTs and demonstrates their non-existence within the considered class.

Findings

No AdS5 x S2 solutions exist in Type IIB supergravity for N=2 SCFT duals.

SU(2) R-symmetry cannot be realized geometrically on S2 in these solutions.

The only U(1) R-symmetry directions are generic Killing vectors, with no special solutions.

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.