Argyres-Douglas Theories and S-Duality

TL;DR

This paper extends S-duality concepts to N=2 superconformal field theories with non-integer Coulomb branch operators, revealing new dualities and exotic SCFTs through gauging procedures and exploring their conformal manifolds.

Contribution

It introduces minimal generalizations of known S-dualities to theories with non-integer scaling dimensions, uncovering novel dualities and emergent SCFTs.

Findings

S-duality acts on parameters similar to Spin(8) triality.

Emergence of an exotic rank-two SCFT in dual descriptions.

Construction of new dualities via gauging flavor symmetries.

Abstract

We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory with four fundamental flavors by Seiberg and Witten and in SU(3) gauge theory with six fundamental flavors by Argyres and Seiberg. Our constructions start by weakly gauging diagonal SU(2) and SU(3) flavor symmetry subgroups of two copies of a particular rank-one Argyres-Douglas theory (along with sufficient numbers of hypermultiplets to guarantee conformality of the gauging). As we explore the resulting conformal manifold of the SU(2) SCFT, we find an action of S-duality on the parameters of the theory that is reminiscent of Spin(8) triality. On the other hand, as we explore the conformal manifold of the SU(3) theory, we find that an exotic rank-two SCFT emerges in a dual SU(2) description.