On the Defect Group of a 6D SCFT

TL;DR

This paper investigates the intrinsic surface defect charges in 6D SCFTs using F-theory, revealing that the defect group is the abelianization of a specific discrete subgroup of U(2), which influences the theory's partition structure.

Contribution

It computes the defect group for all known 6D SCFTs and links it to the abelianization of a discrete subgroup of U(2), providing new insights into the structure of these theories.

Findings

The defect group is the abelianization of a discrete subgroup of U(2).

The defect group measures non-screened surface defect charges.

It determines whether the theory has a partition vector or partition function.

Abstract

We use the F-theory realization of 6D superconformal field theories (SCFTs) to study the corresponding spectrum of stringlike, i.e. surface defects. On the tensor branch, all of the stringlike excitations pick up a finite tension, and there is a corresponding lattice of string charges, as well as a dual lattice of charges for the surface defects. The defect group is data intrinsic to the SCFT and measures the surface defect charges which are not screened by dynamical strings. When non-trivial, it indicates that the associated theory has a partition vector rather than a partition function. We compute the defect group for all known 6D SCFTs, and find that it is just the abelianization of the discrete subgroup of U(2) which appears in the classification of 6D SCFTs realized in F-theory. We also explain how the defect group specifies defining data in the compactification of a (1,0) SCFT.