On the Classification of 6D SCFTs and Generalized ADE Orbifolds
release_xswpxxvgjjcvdfiyqatzjhv72e
by
Jonathan J. Heckman, David R. Morrison, Cumrun Vafa
2014
Abstract
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 / G with G a discrete subgroup of U(2). When G 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 G 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.
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