Hierarchy of RG flows in 6d $(1,0)$ orbi-instantons

TL;DR

This paper maps the hierarchy of RG flows among 6d (1,0) ADE-type orbi-instanton SCFTs, revealing a detailed Hasse diagram structure based on quiver subtraction and Kraft-Procesi transitions.

Contribution

It explicitly determines the full hierarchy of Higgs branch RG flows for type A orbi-instantons, connecting homomorphisms via a novel partial order and diagrammatic approach.

Findings

Hierarchical RG flow structure represented by a Hasse diagram.

Flow relations correspond to Kraft-Procesi transitions between homomorphisms.

Complete characterization of RG flows for all N and k in type A case.

Abstract

$N$ M5-branes probing the intersection between the orbifold $\mathbb{C}^2/\Gamma_\text{ADE}$ and an $E_8$ wall give rise to 6d $(1,0)$ SCFTs known as ADE-type orbi-instantons. At fixed $N$ and order of the orbifold, each element of $\text{Hom}(\Gamma_\text{ADE},E_8)$ defines a different SCFT. The SCFTs are connected by Higgs branch RG flows, which generically reduce the flavor symmetry of the UV fixed point. We determine the full hierarchy of these RG flows for type A, i.e. $\mathbb{C}^2/\mathbb{Z}_k$, for any value of $N$ and $k$. The hierarchy takes the form of an intricate Hasse diagram: each node represents an IR orbi-instanton (homomorphism), and each edge an allowed flow, compatibly with the 6d $a$-theorem. The partial order is defined via quiver subtraction of the 3d magnetic quivers associated with the 6d SCFTs, which is equivalent to performing a so-called Kraft-Procesi transition between homomorphisms.