$K$-theoretic Hall algebras and Coulomb branches

TL;DR

This paper constructs a surjective homomorphism linking the double loop-nilpotent K-theoretic Hall algebra to Coulomb branch algebra in quiver gauge theories, utilizing shuffle algebra interpretation.

Contribution

It introduces a novel connection between K-theoretic Hall algebras and Coulomb branches through a homomorphism based on shuffle algebra methods.

Findings

Established a surjective homomorphism between the two algebraic structures

Utilized shuffle algebra interpretation to facilitate the construction

Bridged K-theoretic Hall algebras with Coulomb branch algebras

Abstract

We construct a surjective homomorphism from the (suitably interpreted) double loop-nilpotent $K$-theoretic Hall algebra to the Coulomb branch algebra of a quiver gauge theory, using the shuffle algebra interpretation.