Microscopic justification of the magnetic-quiver/monopole-formula method for 5d Higgs branches

Establish a microscopic proof that the computation of the Hilbert series via the monopole formula for the Coulomb branch of the three-dimensional N=4 magnetic quiver associated to a five-dimensional braneweb correctly reproduces the Higgs-branch chiral ring of the original five-dimensional N=1 gauge theory, thereby justifying the step from classical 't Hooft–Polyakov monopoles to monopole operators in this context.

Background

The paper relies on the magnetic-quiver/monopole-formula framework to compute Hilbert series and extract generators and relations of the Higgs-branch chiral ring for 5d N=1 theories engineered by brane webs.

The authors acknowledge a logical gap between classical 't Hooft–Polyakov monopoles and the monopole-operator formalism used in the monopole formula and note that a microscopic proof of this identification is still lacking, even though the method matches alternative computations in many cases.