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

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.

v2: typos fixed, references added, improved discussion in section 3.3, version published in JHEP; v1: Part I of a series of papers; 49+31 pages; 25 figures (hi-res figures can be downloaded from the arXiv submission source)

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Cited by in corpus (13)

• Fibrations and Hasse diagrams for 6d SCFTs
• Back to Heterotic Strings on ALE Spaces: Part I -- Instantons, 2-groups and T-duality
• Higgs branch RG-flows via Decay and Fission
• Decay and Fission of Magnetic Quivers
• Hierarchies of RG flows in 6d $(1,0)$ massive E-strings
• The Higgs branch of Heterotic ALE instantons
• A new vista on the Heterotic Moduli Space from Six and Three Dimensions
• Orthosymplectic Quotient Quiver Subtraction
• Quotient Quiver Subtraction
• Atomic Higgsings of 6D SCFTs
• Atomic Higgsings of 6D SCFTs II: Induced Flows
• Quiver Polymerisation
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D