Multiplicative slices, relativistic Toda and shifted quantum affine algebras

TL;DR

This paper introduces shifted quantum affine algebras, explores their structures and actions on K-theoretic Coulomb branches, and relates them to the relativistic Toda lattice, revealing new algebraic and geometric connections.

Contribution

It defines shifted quantum affine algebras, establishes their homomorphisms into Coulomb branches, and connects them to the relativistic Toda lattice in type A.

Findings

Shifted quantum affine algebras map into K-theoretic Coulomb branches.

They act on the equivariant K-theory of parabolic Laumon spaces.

In type A_1, they relate to the open relativistic quantum Toda lattice.

Abstract

We introduce the shifted quantum affine algebras. They map homomorphically into the quantized $K$-theoretic Coulomb branches of $3d\ {\mathcal N}=4$ SUSY quiver gauge theories. In type $A$, they are endowed with a coproduct, and they act on the equivariant $K$-theory of parabolic Laumon spaces. In type $A_1$, they are closely related to the open relativistic quantum Toda lattice of type $A$.