On the Defect Group of a 6D SCFT

TL;DR

This work identifies the defect group of 6D SCFTs realized in F-theory as the abelianization $Ab[\Gamma]$ of the discrete orbifold subgroup $\Gamma\subset U(2)$ that classifies the base geometry. The authors show that the defect group, defined as $\mathcal{C}=\Lambda_{string}^{*}/\Lambda_{string}$, encodes surface defect charges not screened by tensor-branch strings and persists under blowups, making it intrinsic to the SCFT. They compute $\mathcal{C}$ for all known (1,0) theories, obtaining a complete set of ADE-type results and generalized A- and D-type bases, with explicit cyclic or product structures depending on the endpoint data. They also discuss how this discrete data descends under compactification to lower dimensions via flux ensembles and partition vectors, linking 6D defect data to 5D gauge theory global structures and 4D theories. The findings illuminate the discrete topological structure of F-theory vacua and suggest deeper connections to topological field theories and K-theoretic frameworks in string compactifications.

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.