Bethe/Gauge Correspondence for ABCD quiver Gauge Theories and Spin Chains

Abstract

This note is an extension of [DZ23] where the supersymmetric vacua of three-dimensional N = 2 gauge theories with matter are shown to be in one-to-one correspondence with the eigenstate of XXZ integrable spin chain Hamiltonians with open boundary conditions. We consider the A 2 quiver gauge theory, which is the simplest non-trivial quiver gauge theory, and sl 3 open XXZ spin chain with diagonal boundary condition. We demonstrate the correspondence between the vacuum equations of different gauge groups and Bethe ansatz equations with different boundary parameters. We furthermore push forward the program to the general linear quiver gauge theory.

Bethe/Gauge correspondence for ABCDEFG-type 3d gauge theories

“…In this section, we give a swift review of the integrable spin chains at the example of the XXZ spin chain for SU (2). The integrability of a spin chain is characterized by an…”

“…The Bethe ansatz equation of SU(3) spin chain with generic boundary condition has been calculated in [33]. With two gauge nodes being different classical Lie groups, we also consider a higher level A 2 quiver gauge theory and higher rank sl 3 spin chain model in [2]. And we desire the correspondence also materialize with our new methods.…”