On Twisted $A_{2n}$ Class-S Theories

TL;DR

This paper advances the understanding of Coulomb branches in twisted $A_{2n}$ class-S theories by deriving a dimension formula, analyzing puncture contributions, and identifying related 4d $ =2$ SCFTs.

Contribution

It provides a new formula for Coulomb branch dimensions and analyzes puncture contributions, enhancing the understanding of twisted $A_{2n}$ class-S theories.

Findings

Derived a formula for Coulomb branch dimension.

Analyzed puncture contributions to Coulomb branch.

Identified known 4d $ =2$ SCFTs within twisted $A_{2n}$ theories.

Abstract

In this paper, we investigate the twisted $A_{2n}$ sector of class-S theories. Heretofore, the Coulomb branches of such theories have been poorly understood. In this, and a companion paper, we make progress in our understanding of them. In particular, we find a formula for the dimension of the Coulomb branch of any twisted $A_{2n}$ class-S theory. Deferring a systematic analysis to the companion paper, we here determine many contributions of punctures to the graded Coulomb branch dimensions, and in some low rank cases, all of them. We are then able to identify a variety of known 4d $\mathcal{N}=2$ SCFTs with twisted $A_{2n}$ theories, and reproduce many of their known properties, such as S-duality amongst certain Argyres-Douglas theories.