Two Applications of Nilpotent Higgsing in Class-S

TL;DR

This paper explores Higgs-branch RG flows in class-S theories, revealing new insights into current-algebra levels and providing counterexamples to a conjecture about flavor symmetry groups in 4D Ts.

Contribution

It introduces a novel class of Higgsing RG flows in class-S theories and applies them to determine unknown current-algebra levels and challenge existing conjectures.

Findings

Determined current-algebra levels for certain class-S theories.

Constructed pairs of Ts with identical invariants.

Disproved the conjecture linking flavor symmetry group form to isomorphism.

Abstract

We introduce a class of Higgs-branch RG flows in theories of class-S, which flow between $d=4$ $\mathcal{N}=2$ 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 $E_6$ and $E_7$ - and 2) constructing a multitude of examples of pairs of $\mathcal{N}=2$ 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.