A note on supersymmetric AdS_6 solutions of massive type IIA supergravity

TL;DR

The paper addresses the existence and classification of supersymmetric AdS$_6$ backgrounds in massive Type IIA supergravity with an $SO(5,2)$ symmetry. By translating the gravitino and dilatino variations into bilinear relations among Spin$(4)$ spinors, it shows that there is no solution when the four-form flux vanishes ($\,oxed{\mu=0}$), and that the only consistent nonzero-flux case leads to the known warped product $AdS_6\times_w S^4$. The authors explicitly reconstruct the AdS$_6\times_w S^4$ background, deriving its internal $M_4$ as a hemisphere of $S^4$, the explicit warp/dilaton/flux data, and demonstrating that 16 supercharges are preserved with an $SU(2)_R$ isometry realized by Killing vectors. Together, these results suggest a scarcity of supersymmetric AdS$_6$ vacua and underscore the uniqueness (up to orbifolds) of the AdS$_6\times_w S^4$ solution in this setting, with potential implications for the AdS$_6$/CFT$_5$ correspondence.

Abstract

Motivated by the AdS_6/CFT_5 correspondence, we study general supersymmetric solutions of massive type IIA supergravity, consisting of a warped product of six-dimensional anti-de Sitter space AdS_6 with a four-dimensional Riemannian manifold M_4, and fluxes compatible with the SO(5,2) symmetry. We find that the only local solution of this form is the warped AdS_6 x_w S^4 solution, originally discovered by Brandhuber and Oz. We discuss the supersymmetric properties of this solution.