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Coulomb branches of star-shaped quivers

  • Tudor DimofteEmail author
  • Niklas Garner
Open Access
Regular Article - Theoretical Physics
  • 16 Downloads

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.

Keywords

Supersymmetric Gauge Theory Topological Field Theories Differential and Algebraic Geometry 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Mathematics and Center for Quantum Mathematics and Physics (QMAP)UC DavisDavisU.S.A.
  2. 2.Department of Physics and QMAPUC DavisDavisU.S.A.

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