English

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

High Energy Physics - Theory 2025-05-01 v2 Algebraic Geometry Representation Theory

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)(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 E8E_8. Secondly, we leverage the partial order naturally defined on this Hasse diagram to prove the aa-theorem for orbi-instanton Higgs branch RG flows, thereby exhausting the list of cc-theorems in the even-dimensional (supersymmetric) setting.

Cite

@article{arxiv.2312.17178,
  title  = {Proving the 6d a-theorem with the double affine Grassmannian},
  author = {Marco Fazzi and Suvendu Giri and Paul Levy},
  journal= {arXiv preprint arXiv:2312.17178},
  year   = {2025}
}

Comments

v2: typos fixed, improved discussion in sections 1.4, 3.2.5, 4.1, A.1; added appendix C to clarify the connection with the findings of 2401.08757, highlighting the role of massive E-strings in the full Higgs branch of orbi-instantons. v1: Part III of a series of papers. Computer algebra GAP file, along with high resolution vectorized versions of figures 5,6,7 included in submission source

R2 v1 2026-06-28T14:03:57.083Z