Abstract
The 6D (2,0) theory has codimension-one symmetry defects associated to the outer-automorphism group of the underlying the simply-laced Lie algebra of ADE type. 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) nonsimply laced Lie groups. We propose formulas 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.
Highlights
The six-dimensional (2,0) superconformal theories (SCFT) are mysterious quantum field theories that arise either as low energy descriptions of five branes in M-theory or in a decoupling limit of type-IIB string probing ADE singularities [1,2,3]
We review the general untwisted irregular defects, the resulting 4D N 1⁄4 2 SCFTs, as well as their physical data in Sec
We review the description of codimension-two Bogomol’nyi– Prasad–Sommerfield (BPS) defects in 6D (2,0) SCFTs in terms of the Higgs field and explain the class S construction of 4D N 1⁄4 2 SCFTs using the Hitchin system on a Riemann surface with defect insertions
Summary
The six-dimensional (2,0) superconformal theories (SCFT) are mysterious quantum field theories that arise either as low energy descriptions of five branes in M-theory or in a decoupling limit of type-IIB string probing ADE singularities [1,2,3]. A distinguished class of solutions to (1.1) and (1.2), known as the regular-semisimple type, gives rise to irregular codimension-two defects that are in one-to-one correspondence with three-fold quasihomogeneous isolated singularities of the compound Du Val (cDV) type (see Table III).. A distinguished class of solutions to (1.1) and (1.2), known as the regular-semisimple type, gives rise to irregular codimension-two defects that are in one-to-one correspondence with three-fold quasihomogeneous isolated singularities of the compound Du Val (cDV) type (see Table III).6 This connection between the two very different types of singularities is established by the observation that identical 4D N 1⁄4 2 SCFTs are engineered by (i) compactifying (2,0) SCFT on P1 with such a irregular defect inserted, and (ii) the decoupling limit of IIB string probing a cDV singularity.
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