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Proving the 6d a-theorem with the double affine Grassmannian

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arxiv 2312.17178 v2 pith:75BVQTKO submitted 2023-12-28 hep-th math.AGmath.RT

Marco Fazzi , Suvendu Giri , Paul Levy This is my paper · ORCID
classification hep-thmath.AGmath.RT
keywords affinebranchdiagramdoublefirstflowsgrassmannianhasse
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abstract

This paper contains two results of independent interest, the first being more mathematical in nature whereas the second more physical. We first show that the hierarchy of Higgs branch RG flows between the 6d $(1,0)$ SCFTs known as A-type orbi-instantons is given by the Hasse diagram of certain strata and transverse slices in the double affine Grassmannian of $E_8$. Secondly, we leverage the partial order naturally defined on this Hasse diagram to prove the $a$-theorem for orbi-instanton Higgs branch RG flows, thereby exhausting the list of $c$-theorems in the even-dimensional (supersymmetric) setting.

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  1. Atomic Higgsings of 6D SCFTs II: Induced Flows

    hep-th 2025-01 conditional novelty 6.0 of 10

    For 6d SCFTs, atomic endpoint-changing Higgsings (induced flows) are identified with induced nilpotent orbits, and an analogous induction of discrete E8 homomorphisms is physically defined for orbi-instanton theories.

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