Codimension-two defects and Argyres-Douglas theories from outer-automorphism twist in 6d $(2,0)$ theories

TL;DR

This work extends the class S program by incorporating outer-automorphism twists to classify twisted irregular codimension-two defects in 6d $(2,0)$ theories. By analyzing twisted torsion automorphisms and regular semisimple data, the authors classify twisted irregular defects, derive associated Seiberg–Witten geometries, and extract Coulomb spectra and central charges for a broad family of 4d $\mathcal N=2$ Argyres-Douglas theories with non-simply-laced flavor symmetries. They propose explicit formulae for flavor central charges $k_G$ and the conformal central charges $(a,c)$, and demonstrate consistency with Lagrangian and non-Lagrangian cases; for a subclass, they identify the 2d chiral algebra as a W-algebra $W^{k_{2d}}(G,Y)$ and relate the Higgs branch to the associated variety. Together, these results significantly widen the landscape of AD theories arising from twisted irregular defects and provide concrete bridges between 4d SCFT data and 2d VOAs, with potential applications to dualities, exact marginal deformations, and AGT-type correspondences.

Abstract

The 6d $(2,0)$ theory has codimension-one symmetry defects associated to the outer-automorphism group of the underlying ADE Lie algebra. These symmetry defects give rise to twisted sectors of codimension-two defects that are either regular or irregular corresponding to simple or higher order poles of the Higgs field. In this paper, we perform a systematic study of twisted irregular codimension-two defects generalizing our earlier work in the untwisted case. In a class S setup, such twisted defects engineer 4d ${\mathcal N}=2$ superconformal field theories of the Argyres-Douglas type whose flavor symmetries are (subgroups of) non-simply-laced Lie groups. We propose formulae for the conformal and flavor central charges of these twisted theories, accompanied by nontrivial consistency checks. We also identify the 2d chiral algebra (vertex operator algebra) of a subclass of these theories and determine their Higgs branch moduli space from the associated variety of the chiral algebra.

Figures (3)

• Figure 1: Local configurations of the codimension-one symmetry defects (red line) and codimension-two twisted defects (blue dot) on the Riemann surface in a class S setup.
• Figure 2: The class S setup that involves one irregular defect (star) with or without one regular defect (dot) on a sphere. They engineer $J^{(b)}[k]$ and $(J^{(b)}[k],Y)$ theories in Wang:2015mra respectively. Here $J^{(b)}[k]$ labels the irregular defect and $Y$ labels the regular defect.
• Figure 3: The class S setup for twisted theories: one twisted irregular defect (star) and one twisted regular defect (dot) on a sphere.

Theorems & Definitions (18)

• Conjecture 1: Flavor central charge $k_G$
• Conjecture 2: Conformal central charges $a$ and $c$
• Example 1
• Example 2
• Example 3
• Example 4
• Example 5
• Example 6
• Example 7
• Example 8