Abstract
We study the Coulomb branches of 3d mathcal{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 mathcal{A} . Relations among chiral-ring operators, and their deformation quantization, are canonically induced from the embedding into mathcal{A} . In the case of star-shaped quivers — whose Coulomb branches are related to Higgs branches of 4d mathcal{N}=2 theories of Class mathcal{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.
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