Quiver Yangians as Coulomb branch algebras

2025/02/03 by Chen, Tiantai, Li, Wei · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2502.01323

Abstract

For a 3D N=4 gauge theory, turning on the Ω-background in RxR²_ε deforms the Coulomb branch chiral ring into the quantum Coulomb branch algebra, generated by the 1/2-BPS monopoles together with the complex scalar in the vector-multiplet. We conjecture that for a 3D N=4 quiver gauge theory with unitary gauge group, the quantum Coulomb branch algebra can be formulated as the truncated shifted quiver Yangian Y(\widehatQ,\widehatW) based on the triple quiver \widehatQ of the original quiver Q with canonical potential \widehatW. We check this conjecture explicitly for general tree-type quivers Q by considering the action of monopoles on the 1/2-BPS vortex configurations. The Hilbert spaces of vortices approaching different vacua at spatial infinity furnish different representations of the shifted quiver Yangian, and all the charge functions have only simple poles. For quivers beyond tree-type, our conjecture is consistent with known results on special examples.

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