Holography for (1,0) theories in six dimensions
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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=(1,0) 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 $R^4/Z_k \times R$. 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 AdS$_7$ vacua found in a recent classification in type II theories.
Such vacua involve massive IIA regions, and the internal manifold is
topologically $S^3$. 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 AdS$_7$ solution, in the form of an arbitrary number of concentric
shells wrapping round $S^2$'s.