Distinguishing 6d (1,0) SCFTs: an extension to the geometric construction

Abstract

We provide a new extension to the geometric construction of 6d $(1,0)$ SCFTs that encapsulates Higgs branch structures with identical global symmetry but different spectra. In particular, we find that there exist distinct 6d $(1,0)$ SCFTs that may appear to share their tensor branch description, flavor symmetry algebras, and central charges. For example, such subtleties arise for the very even nilpotent Higgsing of $({\mathfrak{so}}_{4k},{\mathfrak{so}}_{4k})$ conformal matter; we propose a method to predict at which conformal dimension the Higgs branch operators of the two theories differ via augmenting the tensor branch description with the Higgs branch chiral ring generators of the building block theories. Torus compactifications of these 6d $(1,0)$ SCFTs give rise to 4d $\mathcal{N}=2$ SCFTs of class $\mathcal{S}$ and the Higgs branch of such 4d theories are captured via the Hall--Littlewood index. We confirm that the resulting 4d theories indeed differ in their spectra in the predicted conformal dimension from their Hall--Littlewood indices. We highlight how this ambiguity in the tensor branch description arises beyond the very even nilpotent Higgsing of $({\mathfrak{so}}_{4k},{\mathfrak{so}}_{4k})$ conformal matter, and hence should be understood for more general classes of 6d $(1,0)$ SCFTs.

28 pages+references, 1 figure, Journal published version

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• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Atomic Higgsings of 6D SCFTs
• Isomorphisms of 4d N=2 SCFTs from 6d
• Atomic Higgsings of 6D SCFTs II: Induced Flows
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Orbi-Instantons and Class $\mathcal{S}$ Theories of Type D