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Classification of Argyres-Douglas theories from M5 branes

Yifan Wang, Dan Xie

TL;DR

This work systematically enlarges the landscape of four-dimensional Argyres-Douglas theories by classifying irregular punctures for the 6d (2,0) ADE theory on a sphere and linking the resulting Hitchin system data to isolated threefold singularities in Type IIB string theory. It introduces a unifying framework that maps irregular puncture data to Coulomb branch spectra and central charges via both Hitchin spectral curves and IIB 3-fold singularities, including maximal irregular cases, degenerations, and outer-automorphism twists. The paper provides explicit constructions across A, D, and E types, including D-type Newton polygon examples and twisted theories, and derives general formulas for central charges, Coulomb spectra, and their limits. The results offer a broad and testable atlas of AD theories with multiple dual descriptions and potential holographic or stringy interpretations, and point to future directions in RG flows, 3d mirrors, surface operators, and Langlands-related structures.

Abstract

We obtain a large class of new 4d Argyres-Douglas theories by classifying irregular punctures for the 6d (2,0) superconformal theory of ADE type on a sphere. Along the way, we identify the connection between the Hitchin system and three-fold singularity descriptions of the same Argyres-Douglas theory. Other constructions such as taking degeneration limits of the irregular puncture, adding an extra regular puncture, and introducing outer-automorphism twists are also discussed. Later we investigate various features of these theories including their Coulomb branch spectrum and central charges.

Classification of Argyres-Douglas theories from M5 branes

TL;DR

This work systematically enlarges the landscape of four-dimensional Argyres-Douglas theories by classifying irregular punctures for the 6d (2,0) ADE theory on a sphere and linking the resulting Hitchin system data to isolated threefold singularities in Type IIB string theory. It introduces a unifying framework that maps irregular puncture data to Coulomb branch spectra and central charges via both Hitchin spectral curves and IIB 3-fold singularities, including maximal irregular cases, degenerations, and outer-automorphism twists. The paper provides explicit constructions across A, D, and E types, including D-type Newton polygon examples and twisted theories, and derives general formulas for central charges, Coulomb spectra, and their limits. The results offer a broad and testable atlas of AD theories with multiple dual descriptions and potential holographic or stringy interpretations, and point to future directions in RG flows, 3d mirrors, surface operators, and Langlands-related structures.

Abstract

We obtain a large class of new 4d Argyres-Douglas theories by classifying irregular punctures for the 6d (2,0) superconformal theory of ADE type on a sphere. Along the way, we identify the connection between the Hitchin system and three-fold singularity descriptions of the same Argyres-Douglas theory. Other constructions such as taking degeneration limits of the irregular puncture, adding an extra regular puncture, and introducing outer-automorphism twists are also discussed. Later we investigate various features of these theories including their Coulomb branch spectrum and central charges.

Paper Structure

This paper contains 24 sections, 110 equations, 6 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Generality about Argyres-Douglas Theories
  3. Basic features
  4. Type IIB construction
  5. Classification of Irregular Singularities
  6. $A$ type irregular singularities
  7. General case
  8. Maximal irregular singularity
  9. Degeneration of irregular singularities
  10. Some Explicit Examples of AD Theories
  11. $D$ type AD theories and Newton polygon
  12. An irregular singularity and an regular singularity
  13. Twisted Irregular Singularity
  14. Review of regular twisted singularities
  15. Maximal twisted irregular singularities
  16. ...and 9 more sections

Figures (6)

  • Figure 1: Regular punctures of $A_3$ theories.
  • Figure 2: Type I and II irregular singularities in $A_2$ theories with $r={4\over 3}$ and $r={1}$ respectively.
  • Figure 3: Connection between AD theory, cDV singularity, and Hitchin system.
  • Figure 4: Newton polygons for $D_4^{(6)}[5]$ and $D_4^{(4)}[6]$ theories.
  • Figure 5: Newton Polygons for $(D_4^{(6)}[5],F)$ and $(D_4^{(4)}[6],F)$ theories.
  • ...and 1 more figures