Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
Generators for Coulomb branches of quiver gauge theories
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abstract
We study the Coulomb branches of $3d$ $\mathcal{N}=4$ quiver gauge theories, focusing on the generators for their quantized coordinate rings. We show that there is a surjective map from a shifted Yangian onto the quantized Coulomb branch, once the deformation parameter is set to $\hbar =1$. In finite ADE type, this extends to a surjection over $\mathbb{C}[\hbar]$. We also show that these algebras are generated by the dressed minuscule monopole operators, for an arbitrary quiver (this is similar to the proof of Theorem 4.29 in arXiv:1811.12137). Finally, we describe how the KLR Yangian algebra from arXiv:1806.07519 is related to Webster's extended BFN category. This paper provides proofs for two results which were announced in arXiv:1806.07519.
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UNVERDICTED 2representative citing papers
Constructs a surjective homomorphism from the double loop-nilpotent K-theoretic Hall algebra to the Coulomb branch algebra of a quiver gauge theory using shuffle algebra methods.
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Quiver Yangians as Coulomb branch algebras
Conjectures that quantum Coulomb branch algebras of 3D N=4 unitary quiver gauge theories equal truncated shifted quiver Yangians Y(ˆQ, ˆW), verified explicitly for tree-type quivers via monopole actions on 1/2-BPS vortices.
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$K$-theoretic Hall algebras and Coulomb branches
Constructs a surjective homomorphism from the double loop-nilpotent K-theoretic Hall algebra to the Coulomb branch algebra of a quiver gauge theory using shuffle algebra methods.