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.
Highlights
A striking prediction of string compactification is the existence of interacting conformal fixed points in six dimensions
As should be clear, there is a rich class of 6D superconformal field theories (SCFTs) which can be realized in F-theory
In this paper we have studied geometrically realized superconformal field theories which can arise in compactifications of F-theory
Summary
A striking prediction of string compactification is the existence of interacting conformal fixed points in six dimensions. Using the classification results on “non-Higgsable” six-dimensional F-theory models [21] and by determining how these non-Higgsable clusters can couple to one another (i.e., their compatibility with the elliptic fibration) we find that the configuration of such curves reduces to an ADE graph consisting of just curves with self-intersection −2, or a generalized A- or D-type graph of curves where the self-intersection can be less than −2. A minimal 6D SCFT can be used to construct non-minimal SCFTs by bringing in additional ingredients: we can bring in a number of E-string theories and/or make the Kodaira-Tate type of the fiber over the curves more singular This amounts to decorating curves in the base with a self-consistent choice of gauge algebra. In addition to the non-Higgsable clusters which carry a gauge symmetry, we can have isolated configurations without a gauge group These are given by −2 curves which intersect according to an ADE Dynkin diagram.
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