Quantum Higgs branches of isolated $\mathcal{N}=2$ superconformal field theories

Abstract

We study the Higgs branches of the superconformal points of four-dimensional $\mathcal{N}=2$ super Yang-Mills (SYM) which appear due to the occurrence of mutually local monopoles having appropriate charges. We show, for example, that the maximal superconformal point of SU(2n) SYM has a Higgs branch of the form ${{{{{\mathbb{C}}^2}}} \left/ {{{{\mathbb{Z}}_n}}} \right.}$. These Higgs branches are intrinsic to the superconformal field theory (SCFT) at the superconformal point, but do not appear in the SYM theory in which it is embedded. This is because the embedding is a UV extension of the SCFT in which some global symmetry acting on the Higgs branch is gauged irrelevantly. Higgs branches deduced from earlier direct studies of these isolated SCFTs using BPS wall-crossing or 3-d mirror symmetry agree with the ones we find here using just the Seiberg-Witten data for the SYM theories.