Quiver Yangians as Coulomb branch algebras

TL;DR

This paper proposes a new algebraic framework, the truncated shifted quiver Yangian, to describe the quantum Coulomb branch of 3D N=4 quiver gauge theories, and verifies it for tree-type quivers.

Contribution

It introduces the conjecture that the quantum Coulomb branch algebra for unitary quiver gauge theories is given by the truncated shifted quiver Yangian, extending known results.

Findings

Verified the conjecture for general tree-type quivers Q.

Demonstrated the action of monopoles on vortex configurations.

Established the correspondence between vortex Hilbert spaces and shifted quiver Yangian representations.

Abstract

For a 3D N=4 gauge theory, turning on the $\Omega$-background in RxR$^2_{\epsilon}$ 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$(\widehat{Q},\widehat{W})$ based on the triple quiver $\widehat{Q}$ of the original quiver Q with canonical potential $\widehat{W}$. 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.