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Title: Two Applications of Nilpotent Higgsing in Class-S
We introduce a class of Higgs-branch RG flows in theories of class-S, 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 current-algebra levels in SCFTs where they were previously unknown — a program we carry out for the class-S 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.
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