AdS_6 solutions of type II supergravity

TL;DR

This paper classifies all possible supersymmetric AdS_6 solutions in type IIB supergravity using pure spinor techniques, reducing the problem to two PDEs and exploring their relation to fivebrane web configurations.

Contribution

It provides a complete classification of AdS_6 solutions in type IIB supergravity, extending the understanding of such backgrounds and their dual CFTs.

Findings

Classified AdS_6 solutions in type IIB supergravity.

Reduced the problem to two PDEs on a two-dimensional space.

Showed no AdS_6 solutions exist in eleven-dimensional supergravity.

Abstract

Very few AdS_6 x M_4 supersymmetric solutions are known: one in massive IIA, and two IIB solutions dual to it. The IIA solution is known to be unique; in this paper, we use the pure spinor approach to give a classification for IIB supergravity. We reduce the problem to two PDEs on a two-dimensional space Sigma. M_4 is then a fibration of S^2 over Sigma; the metric and fluxes are completely determined in terms of the solution to the PDEs. The results seem likely to accommodate near-horizon limits of (p,q)-fivebrane webs studied in the literature as a source of CFT_5's. We also show that there are no AdS_6 solutions in eleven-dimensional supergravity.