New rank-2 Argyres-Douglas theory

Justin Kaidi,Mario Martone

doi:10.1103/physrevd.104.085004

Abstract

We provide evidence for the existence of a new strongly-coupled four dimensional $\mathcal{N}=2$ superconformal field theory arising as a non-trivial IR fixed point on the Coulomb branch of the mass-deformed superconformal Lagrangian theory with gauge group $G_2$ and four fundamental hypermultiplets. Notably, our analysis proceeds by using various geometric constraints to bootstrap the data of the theory, and makes no explicit reference to the Seiberg-Witten curve. We conjecture a corresponding VOA and check that the vacuum character satisfies a linear modular differential equation of fourth order. We also propose an identification with existing class $\mathcal{S}$ constructions.

Highlights

Among 4d N 1⁄4 2 superconformal field theories (SCFTs), of particular interest are those with some chiral ring generators having fractional scaling dimension
Several other means of obtaining such theories have been developed, and in particular constructions in class S and geometric engineering [2,3,4] have allowed one to circumvent the Lagrangian starting point altogether, giving rise to a wealth of Argyres-Douglas (AD) type theories which are not connected in any obvious way to the moduli space of known Lagrangian theories
We will use a variety of geometric constraints on the structure of the Coulomb and Higgs branches to bootstrap the data of the theory

Summary

INTRODUCTION

Among 4d N 1⁄4 2 superconformal field theories (SCFTs), of particular interest are those with some chiral ring generators having fractional scaling dimension Such theories are necessarily non-Lagrangian and as such are not amenable to study by the most naive means. Several other means of obtaining such theories have been developed, and in particular constructions in class S and geometric engineering [2,3,4] have allowed one to circumvent the Lagrangian starting point altogether, giving rise to a wealth of Argyres-Douglas (AD) type theories which are not connected in any obvious way to the moduli space of known Lagrangian theories. We will use a variety of geometric constraints on the structure of the Coulomb and Higgs branches to bootstrap the data of the theory This will allow us to construct a consistent candidate moduli space, as well as a corresponding vertex operator. Our example serves as a proof of principle that a bottom-up, geometric approach to bootstrapping general N 1⁄4 2 SCFTs in 4d is feasible

GEOMETRIC ANALYSIS

ALGEBRAIC ANALYSIS

ADðc2Þ

High-temperature limit

CLASS S CONSTRUCTION