Brane Webs and Magnetic Quivers for SQCD

TL;DR

This paper uses magnetic quivers and brane web techniques to analyze the Higgs branch structure of 4d $ ext{N}=2$ SQCD, revealing its decomposition into cones, the role of nilpotent operators, and the global symmetries involved.

Contribution

It introduces magnetic quivers for five-brane webs as a new method to study the Higgs branch of 4d $ ext{N}=2$ SQCD, providing new insights and confirming results with Hilbert series computations.

Findings

Magnetic quivers accurately reproduce the Higgs branch structure.

Decomposition of the Higgs branch into baryonic and mesonic cones identified.

Conjectures for the Hilbert series of the full Higgs branch proposed.

Abstract

It is widely considered that the classical Higgs branch of 4d $\mathcal{N}=2$ SQCD is a well understood object. However there is no satisfactory understanding of its structure. There are two complications: (1) the Higgs branch chiral ring contains nilpotent elements, as can easily be checked in the case of $\mathrm{SU}(N)$ with 1 flavour. (2) the Higgs branch as a geometric space can in general be decomposed into two cones with nontrivial intersection, the baryonic and mesonic branches. To study the second point in detail we use the recently developed tool of magnetic quivers for five-brane webs, using the fact that the classical Higgs branch for theories with 8 supercharges does not change through dimensional reduction. We compare this approach with the computation of the hyper-K\"ahler quotient using Hilbert series techniques, finding perfect agreement if nilpotent operators are eliminated by the computation of a so called radical. We study the nature of the nilpotent operators and give conjectures for the Hilbert series of the full Higgs branch, giving new insights into the vacuum structure of 4d $\mathcal{N}=2$ SQCD. In addition we demonstrate the power of the magnetic quiver technique, as it allows us to identify the decomposition into cones, and provides us with the global symmetries of the theory, as a simple alternative to the techniques that were used to date.