A tale of two cones: the Higgs Branch of Sp(n) theories with 2n flavours

TL;DR

This paper reveals that the Higgs branch of certain 4d N=2 theories with SO(2N) flavor symmetry is a union of two hyperkahler cones intersecting in a subvariety, challenging the usual single-cone assumption.

Contribution

It demonstrates that the Higgs branch can be a union of two cones with a specified intersection, providing new insights into the structure of Higgs branches in these theories.

Findings

Higgs branch is a union of two hyperkahler cones

Intersection of the cones is a hyperkahler subvariety

This phenomenon impacts understanding of meson-generated Higgs branches

Abstract

The purpose of this short note is to highlight a particular phenomenon which concerns the Higgs branch of a certain family of 4d N = 2 theories with SO(2N) flavour symmetry. By studying the Higgs branch as an algebraic variety through Hilbert series techniques we find that it is not a single hyperkahler cone but rather the union of two cones with intersection a hyperkahler subvariety which we specify. This remarkable phenomenon is not only interesting per se but plays a crucial role in understanding the structure of all Higgs branches that are generated by mesons.