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Argyres-Douglas Theories in Class S Without Irregularity

by Christopher Beem, Wolfger Peelaers

This Submission thread is now published as SciPost Phys. 12, 172 (2022)

Submission summary

As Contributors: Christopher Beem
Arxiv Link: (pdf)
Date accepted: 2022-05-02
Date submitted: 2022-02-03 14:14
Submitted by: Beem, Christopher
Submitted to: SciPost Physics
Academic field: Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We make a preliminary investigation into twisted $A_{2n}$ theories of class S. Contrary to a common piece of folklore, we establish that theories of this type realise a variety of models of Argyres-Douglas type while utilising only regular punctures. We present an in-depth analysis of all twisted $A_2$ trinion theories, analyse their interrelations via partial Higgsing, and discuss some of their generalised S-dualities.

Published as SciPost Phys. 12, 172 (2022)

Submission & Refereeing History

Published as SciPost Phys. 12, 172 (2022)

Reports on this Submission

Anonymous Report 2 on 2022-4-24 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2005.12282v1, delivered 2022-04-24, doi: 10.21468/SciPost.Report.4981


The interpretation of the twisted $A_{2n} $ theories of class-S has proven somewhat mysterious. If one applies the standard formulae for the scaling dimensions of the Coulomb branch generator (along with the rest of the standard formulae that the authors claim are still correct), one rapidly runs into contradictions. The resolution, according to the present authors is that the $U(1)$ r-charges of the Coulomb branch generators are modified from the "naive" ones (where the r-charge of a meromorphic $k$-differential on C is $k$). Instead, the r-charges can be fractional, as in Argyres-Douglas theories.

In the usual formulation of Argyres-Douglas theories (on the sphere, where the Higgs field has an irregular singularity at a point), the modification is well-understood: the r-charge of the infrared SCFT is a linear combination of the "usual" one (which comes from the partial topological twist) and the U(1) isometry of the twice-punctured sphere. Here, the origin of the modification is more mysterious. Indeed, not just the r-charges, but even the number of Coulomb branch generators differs from the "naive" answer.

Clearly, while many mysteries remain, this paper represents a big step forward and should be published.

  • validity: -
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Anonymous Report 1 on 2022-2-26 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:2005.12282v1, delivered 2022-02-26, doi: 10.21468/SciPost.Report.4525


1. The article contains new, interesting, and useful results.
2. The results are stated clearly and explicitly, making the article useful as a reference.
3. The material is well-presented.


This article examined a number of theories of class $\mathcal{S}$ associated with a sphere with regular punctures. The authors demonstrated that certain superconformal field theories (SCFTs) of the Argyres-Douglas type can be engineered in this way. Moreover a new rank-two SCFT, dubbed the $\tilde{T}_3$ theory, was proposed by the authors of this article. Later it has been found that this theory can in fact be realized as a theory on two D3 branes probing an exceptional $E_6$ seven-brane singularity in the presence of an $\mathcal{S}$-fold without flux. For the theories explored in this article, their vertex operator algebras have been studied in-depth and the Schur indices have been computed. Since this article contains interesting and useful results, it deserves publication in the SciPost.

  • validity: -
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: perfect

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