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

TL;DR

This paper systematically studies twisted irregular codimension-two defects in 6d (2,0) theories, revealing their role in engineering 4d Argyres-Douglas SCFTs with non-simply-laced flavor symmetries and analyzing their chiral algebras and moduli spaces.

Contribution

It generalizes the classification of twisted irregular defects and proposes formulas for their central charges, connecting 6d defects to 4d Argyres-Douglas theories with non-simply-laced symmetries.

Findings

Derived formulas for conformal and flavor central charges.

Identified the 2d chiral algebra of certain twisted theories.

Determined Higgs branch moduli spaces from associated varieties.

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.