Coulomb Branches of Star-Shaped Quivers

TL;DR

This paper analyzes the Coulomb branches of star-shaped quiver gauge theories using algebraic techniques, revealing new relations and quantizations, and connecting to 4d N=2 theories of Class S.

Contribution

It introduces a systematic algebraic approach to study Coulomb branches of star-shaped quivers, including new relations and quantizations, extending previous understanding.

Findings

Embedded Coulomb-branch chiral ring into a simpler abelian algebra

Derived relations among chiral-ring operators and their quantizations

Discovered new families of relations in the quantized setting

Abstract

We study the Coulomb branches of 3d N=4 `star-shaped' quiver gauge theories and their deformation quantizations, by applying algebraic techniques that have been developed in the mathematics and physics literature over the last few years. The algebraic techniques supply an abelianization map, which embeds the Coulomb-branch chiral ring into a vastly simpler abelian algebra A. Relations among chiral-ring operators, and their deformation quantization, are canonically induced from the embedding into A. In the case of star-shaped quivers -- whose Coulomb branches are related to Higgs branches of 4d N=2 theories of Class S -- this allows us to systematically verify known relations, to generalize them, and to quantize them. In the quantized setting, we find several new families of relations.