We provide a new extension to the geometric construction of 6d (1, 0) SCFTs that encap sulates 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 (so4k,so4k) conformal matter; we pro pose 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 N = 2 SCFTs of class S and the Higgs branch of such 4d theories are cap tured 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 (so4k,so4k) conformal matter, and hence should be understood for more general classes of 6d (1, 0) SCFTs.
Two Applications of Nilpotent Higgsing in ClassS
We introduce a class of Higgsbranch RG flows in theories of classS, which flow between d = 4 N = 2 SCFTs of the same ADE type. We discuss two applications of this class of RG flows: 1) determining the currentalgebra levels in SCFTs where they were previously unknown — a program we carry out for the classS theories of type E6 and E7 — and 2) constructing a multitude of examples of pairs of N = 2 SCFTs whose “conventional invariants” coincide. We disprove the conjecture of [1] that the global form of the flavour symmetry group is a reliable diagnostic for determining when two such theories are isomorphic.
 Award ID(s):
 1914679
 Publication Date:
 NSFPAR ID:
 10339045
 Journal Name:
 ArXivorg
 ISSN:
 23318422
 Sponsoring Org:
 National Science Foundation
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