Holography for (1,0) theories in six dimensions

M-theory and string theory predict the existence of many six-dimensional SCFTs. In particular, type IIA brane constructions involving NS5-, D6- and D8-branes conjecturally give rise to a very large class of N=10$$ \mathcal{N}=\left(1,0\right) $$ CFTs in six dimensions. We point out that these theories sit at the end of RG flows which start from six-dimensional theories which admit an M-theory construction as a M5 stack transverse to ℝ4/ℤk×ℝ$$ {\mathrm{\mathbb{R}}}^4/{\mathrm{\mathbb{Z}}}_k\times \mathrm{\mathbb{R}} $$. The flows are triggered by Higgs branch expectation values and correspond to D6’s opening up into transverse D8-branes via a Nahm pole. We find a precise correspondence between these CFT’s and the AdS7 vacua found in a recent classification in type II theories. Such vacua involve massive IIA regions, and the internal manifold is topologically S3. They are characterized by fluxes for the NS three-form and RR two-form, which can be thought of as the near-horizon version of the NS5’s and D6’s in the brane picture; the D8’s, on the other hand, are still present in the AdS7 solution, in the form of an arbitrary number of concentric shells wrapping round S2’s.