On the global symmetries of 6D superconformal field theories

TL;DR

This paper investigates the global symmetry groups of 6D superconformal field theories, combining Coulomb branch analysis with F-theory constructions, revealing cases where F-theory models do not fully realize the predicted symmetries.

Contribution

It provides an upper bound for the global symmetry of 6D SCFTs and compares theoretical predictions with F-theory realizations, highlighting discrepancies.

Findings

Most F-theory models realize the predicted global symmetries.

Some cases show F-theory models fail to realize the full symmetry.

A unique case where only subgroups of the predicted symmetry are realized.

Abstract

We study global symmetry groups of six-dimensional superconformal field theories (SCFTs). In the Coulomb branch we use field theoretical arguments to predict an upper bound for the global symmetry of the SCFT. We then analyze global symmetry groups of F-theory constructions of SCFTs with a one-dimensional Coulomb branch. While in the vast majority of cases, all of the global symmetries allowed by our Coulomb branch analysis can be realized in F-theory, in a handful of cases we find that F-theory models fail to realize the full symmetry of the theory on the Coulomb branch. In one particularly mysterious case, F-theory models realize several distinct maximal subgroups of the predicted group, but not the predicted group itself.