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A new rank-2 Argyres-Douglas theory

Justin Kaidi, Mario Martone

TL;DR

The paper proposes a new rank-2 Argyres-Douglas theory ${\rm AD}({{\mathfrak{c}}_2})$ as an IR fixed point on the Coulomb branch of a mass-deformed $G_2$ gauge theory with four fundamentals, built without invoking the Seiberg-Witten curve. It bootstraps the Higgs and Coulomb branch data using geometric constraints, computes a consistent central-charge and flavor data set, and identifies a corresponding VOA that requires an extension of $\widehat{\mathfrak{sp}(4)}_{-{13}/{6}}$ by four dimension-$\tfrac{3}{2}$ generators. The Schur index and its Higgsing limit corroborate the Higgs/Coulomb data, while the vacuum character satisfies a degree-4 modular differential equation with $(c_{2d},h_1,h_2)=(-26,-\tfrac{4}{3},-\tfrac{7}{6})$, supporting the proposed VOA. A Class ${\mathcal S}$ construction from the $A_4$ (2,0) theory on a two-punctured sphere with an irregular puncture and a $\mathbb{Z}_2$ twist matches the central charges, Higgs branch, and flavor data, reinforcing the non-Lagrangian interpretation and expanding the landscape of Argyres-Douglas theories.

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.

A new rank-2 Argyres-Douglas theory

TL;DR

The paper proposes a new rank-2 Argyres-Douglas theory as an IR fixed point on the Coulomb branch of a mass-deformed gauge theory with four fundamentals, built without invoking the Seiberg-Witten curve. It bootstraps the Higgs and Coulomb branch data using geometric constraints, computes a consistent central-charge and flavor data set, and identifies a corresponding VOA that requires an extension of by four dimension- generators. The Schur index and its Higgsing limit corroborate the Higgs/Coulomb data, while the vacuum character satisfies a degree-4 modular differential equation with , supporting the proposed VOA. A Class construction from the (2,0) theory on a two-punctured sphere with an irregular puncture and a twist matches the central charges, Higgs branch, and flavor data, reinforcing the non-Lagrangian interpretation and expanding the landscape of Argyres-Douglas theories.

Abstract

We provide evidence for the existence of a new strongly-coupled four dimensional 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 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 constructions.

Paper Structure

This paper contains 7 sections, 24 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Geometric Analysis: Higgs and Coulomb branch
  3. Algebraic analysis: Schur index and VOA
  4. Schur Index and Higgsing
  5. VOA
  6. High-temperature limit
  7. Class ${\mathcal{S}}$ construction

Figures (3)

  • Figure 1: Hasse diagrams for the CB and HB of $\mathfrak{g}_2 + 4 F$.
  • Figure 2: Relevant conformal data for $\rm AD({{\mathfrak{c}}_2})$.
  • Figure 3: Hasse diagrams for the moduli space of $\rm AD({{\mathfrak{c}}_2})$.