Coulomb Branches of Star-Shaped Quivers

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.

arXiv comment63 pages + appendices; added references

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• Mirror symmetry and line operators
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• Generators for Coulomb branches of quiver gauge theories
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Nonabelian Mirror Symmetry Beyond the Chiral Ring
• Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing Phenomena in 3d $\mathcal{N}=4$ Theories