On the classification of 6D SCFTs and generalized ADE orbifolds

We study (1, 0) and (2, 0) 6D superconformal field theories (SCFTs) that can be constructed in F-theory. Quite surprisingly, all of them involve an orbifold singularity C-2/Gamma with Gamma a discrete subgroup of U(2). When Gamma is a subgroup of SU (2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2, 0) SCFTs. For more general U(2) subgroups, the allowed possibilities for Gamma are not arbitrary and are given by certain generalizations of the A- and D- series. These theories should be viewed as the minimal 6D SCFTs. We obtain all other SCFTs by bringing in a number of E-string theories and/or decorating curves in the base by non-minimal gauge algebras. In this way we obtain a vast number of new 6D SCFTs, and we conjecture that our construction provides a full list.