Argyres-Douglas matter and N=2 dualities

TL;DR

This paper explores S duality in four-dimensional N=2 Argyres-Douglas theories, revealing a sequence of SCFTs and their geometric interpretation via sphere decompositions, connecting different gauge theory descriptions.

Contribution

It introduces a new classification of Argyres-Douglas theories using (p,q) sequences and interprets S duality through geometric decompositions of punctured spheres.

Findings

Identification of a (p,q) sequence of SCFTs with co-prime integers.

Representation of theories via spheres with marked points and pants decompositions.

Connection between dualities and geometric decompositions of punctured spheres.

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.