Spin Thresholds, RG Flows, and Minimality in 4D $\mathcal{N}=2$ QFT

TL;DR

This paper explores the simplicity and RG flow invariants of the minimal Argyres-Douglas (MAD) theory in 4D $ abla=2$ supersymmetric QFT, revealing large spin thresholds shared with free theories and their generalizations.

Contribution

It uncovers the invariance of large spin thresholds under RG flows in MAD and related theories, providing new insights beyond Seiberg-Witten analysis.

Findings

MAD shares infinite large spin thresholds with free $ abla=2$ Maxwell theory.

MAD has the fewest Schur operators among all unitary $ abla=2$ theories.

Large spin thresholds encode RG flows in $(A_1, A_{2k})$ theories.

Abstract

Long ago, Argyres and Douglas discovered a particularly simple interacting 4D $\mathcal{N}=2$ superconformal field theory (SCFT) on the Coulomb branch of $SU(3)$ $\mathcal{N}=2$ super Yang-Mills. Further hints of the theory's simplicity arise due to the fact that it has the smallest possible value of the $c$ central charge among unitary interacting $\mathcal{N}=2$ SCFTs. A main purpose of this note is to uncover additional aspects of this minimal Argyres-Douglas (MAD) theory's simplicity. In particular, we argue that: (1) the MAD theory shares an infinite set of large spin thresholds in part of its operator spectrum with the free $\mathcal{N}=2$ Maxwell theory (this data is therefore invariant under generic $\mathcal{N}=2$-preserving renormalization group flows to the IR) and (2) the MAD theory has, at every order in the natural grading, the smallest number of "Schur" operators of any unitary $\mathcal{N}=2$ theory (interacting or free). We then show that property (1) has a suitable generalization for all $(A_1, A_{2k})$ cousins of the MAD theory. In particular, the corresponding large spin thresholds encode generic renormalization group flows within this class. This construction therefore gives a different handle on these flows from the one provided by the Seiberg-Witten description. To emphasize the importance of these spin thresholds, we abstractly study theories with "enough matter" to form Higgs branches and argue that infinitely many spin thresholds are small or vanishing.