On SUSY-breaking moduli spaces of AdS7 vacua and 6D SCFTs

We study supersymmetric AdS7 vacua of massive type IIA string theory, which were argued to describe the near-horizon limit of NS5/D6/D8-brane intersections and to be holographically dual to 6D (1,0) theories. We show, for the case without D8-brane charges, that such vacua do not admit any supersymmetry-breaking deformations. Our result implies that the dual (1, 0) theories do not have a conformal manifold, thus extending previously known results for supersymmetric deformations. It is also in line with the recent conjecture that non-supersymmetric AdS vacua are in the swampland.