General Argyres-Douglas Theory

TL;DR

The paper develops a comprehensive framework to generate Argyres-Douglas type 4d N=2 SCFTs by compactifying 6d (2,0) theories on Riemann spheres with irregular singularities, classifying admissible singularities and deriving Seiberg-Witten curves and operator spectra from Hitchin-system data. It shows how fractional Coulomb-branch dimensions and dimensional couplings arise naturally from higher-order poles and explains central charges a and c via 3d mirror symmetry and a universal R(B) structure, validating results against known AD examples and novel families. The authors extend the construction to A2 and higher-rank theories, derive 3d mirrors, explore UV completions and SU(3) QCD connections, and propose equivalences among seemingly different irregular realizations (including Type II/IV and Type I/IV dualities). The work significantly broadens the landscape of N=2 SCFTs, providing tools for further exploration of dualities, gravity duals, AGT-type correspondences, and cluster-coordinate formulations for AD theories.

Abstract

We construct a large class of Argyres-Douglas type theories by compactifying six dimensional (2,0) A_N theory on a Riemann surface with irregular singularities. We give a complete classification for the choices of Riemann surface and the singularities. The Seiberg-Witten curve and scaling dimensions of the operator spectrum are worked out. Three dimensional mirror theory and the central charges a and c are also calculated for some subsets, etc. Our results greatly enlarge the landscape of N=2 superconformal field theory and in fact also include previous theories constructed using regular singularity on the sphere.

Figures (20)

• Figure 1: The Newton polygon representing an irregular singularity, and each segment on the boundary represents a block and its slope is the order of pole of that block.
• Figure 2: Left: The Newton polygon for the irregular singularity with only one block and this is the case $a$ and $c$. Right: The leading order has partition $[N-1, 1]$, this is the case $b$.
• Figure 3: Left: A graph representation of $(A_1, A_5)$ theory, scale invariance is used to fix the coefficient of $z^6$ term to be 1 and translation invariance is used to eliminate $z^5$ term; Right: A graph representation for $(A_1, D_7)$ theory, notice that $z^5$ term is turned on as the coupling constant.
• Figure 4: (a): Quiver for type I irregular singularity with order $n$, there are $n-2$ bifundamentals between two $U(1)$ groups, this is the 3d mirror for $(A_1, A_{N-1})$ theory, here $N=2n-4$; b): Quiver leg for a regular singularity; c): We spray the $U(2)$ flavor symmetry of $(b)$ to two $U(1)$s so that we can glue this tail to the quiver in $(a)$; d): Gluing quiver tail in $c$ and the quiver in $a$ which is the three dimensional mirror for $(A_, D_{N+2})$ theory.
• Figure 5: A) The Hitchin system for various SU(2) QCDs, black dots represent type II irregular singularity; Circle represents type I irregular singularity; Cross represents the regular singularity. The number is the integer part of the order of pole. B) The singularity structure for the corresponding AD theory found from the above QCD.