Argyres-Douglas matter and N=2 dualities

TL;DR

This work extends S-duality for four-dimensional N=2 Argyres-Douglas theories by introducing a coprime $(p,q)$ labeling and a sphere-with-marked-points (pants) framework in which S-duality corresponds to degeneration into three-punctured spheres. It develops class $(p,1)$ and general class $(p,q)$ theories via irregular and regular Hitchin punctures, derives the Seiberg-Witten data from Newton polygons, and constructs explicit 3d mirrors to access dual frames and flavor symmetries. The authors perform consistency checks by matching Coulomb branch spectra, central charges, and beta-function constraints across dual frames, and they discuss gauging AD matter to build broader SCFTs while noting genus extensions are not generically possible. This generalizes class ${\cal S}$ to a wider family of $\mathcal{N}=2$ theories and offers a tractable, string-inspired handle on their nonperturbative dualities and observables.

Abstract

We study S duality of four dimensional N=2 Argyres-Douglas (AD) theory engineered from 6d A_{N-1} (2,0) theory. We find a (p,q) sequence of SCFTs, here (p,q) is co-prime and class S theory defined on sphere corresponds to class (0,1) theory. We represent these theories by a sphere with marked points, and S duality is interpreted as different pants decompositions of the same punctured sphere. The weakly coupled gauge theory description involves gauging AD matter which is represented by three punctured sphere.

Figures (24)

• Figure 1: $(A_3, A_5)$ theory is represented by a sphere with four marked points, here we need to use three types of marked points besides the Young Tableaux data. This theory belongs to class $(3,2)$ theory, and its weakly coupled gauge theory description can be found from the degeneration limit of the punctured sphere. There are two duality frames as we can only exchange two black marked points.
• Figure 2: Newton polygon of SCFT defined by 6d $A_{N-1}$$(2,0)$ theory on a sphere with an irregular singularity and a regular singularity. The SW curve can be found from the monomials associated with black bullets within Newton polygon.
• Figure 3: Young Tableaux with labels. Here $Y_3=[2,2,2],Y_2=[2,2,2], Y_1=[1,1,1,1,1,1]$.
• Figure 4: Step 1: If the first Young Tableaux $Y_n$ has partition $[n_1, n_2, n_3]$, first assign a quiver with three nodes and ranks $n_i$, and then connect $n-2$ quiver arrows between those nodes. Step 2: If $n_1$ is further partitioned into $[m_1, m_2]$ in $Y_{n-1}$, we split the quiver node with rank $n_1$ into two quiver nodes with rank $m_1$ and $m_2$, and the number of quiver arrows between $m_i$ and $n_1$, $n_2$ are still $n-2$; but the number of arrows between $m_1$ and $m_2$ are $n-3$. Similar procedure is done for other Young Tableaux and we stop at $Y_2$. Bottom: If a column with height $l$ in $Y_2$ is further split into $[l_1, l_2,\ldots,l_t]$, one attach a quiver tail to the node with rank $l$ in quiver determined by $(Y_n,\ldots Y_2)$; For $Y_0$, we attach a quiver tail which is connected to all the quiver nodes determined by $Y_2$. The number of quiver arrow is one if there is no label.
• Figure 5: Left: 3d mirror for theory $(A_{3}; Y_{n}, \ldots, Y_{1}; Y_0)$ with $Y_n=\ldots=Y_1=[1,1,1,1]$ and $Y_0=[4]$ (trivial). Right: 3d mirror for theory $(A_{3}; Y_{n}, \ldots, Y_{1}; Y_0)$ with $Y_n=\ldots=Y_1=[1,1,1, 1]$ and $Y_0=[1,1,1,1]$. The number of quiver arrow is one if there is no label.

Theorems & Definitions (1)

• Conjecture 1