Expanding the Bethe/Gauge Dictionary

TL;DR

This paper extends the Bethe/Gauge correspondence by linking algebraic Bethe ansatz elements to supersymmetric gauge theories, constructing Bethe wave functions as defects, and relating R-matrices to interface correlation functions.

Contribution

It introduces a new framework connecting off-shell Bethe states with orbifold defects and boundary conditions in supersymmetric theories, enriching the Bethe/Gauge dictionary.

Findings

Bethe wave functions realized as orbifold defects

Off-shell Bethe states described as boundary conditions

Spin chain R-matrices interpreted as interface correlation functions

Abstract

We expand the Bethe/Gauge dictionary between the XXX Heisenberg spin chain and 2d N = (2,2) supersymmetric gauge theories to include aspects of the algebraic Bethe ansatz. We construct the wave functions of off-shell Bethe states as orbifold defects in the A-twisted supersymmetric gauge theory and study their correlation functions. We also present an alternative description of off-shell Bethe states as boundary conditions in an effective N = 4 supersymmetric quantum mechanics. Finally, we interpret spin chain R-matrices as correlation functions of Janus interfaces for mass parameters in the supersymmetric quantum mechanics.