Spectral dualities in XXZ spin chains and five dimensional gauge theories

TL;DR

This paper explores spectral dualities in XXZ spin chains and their relation to five-dimensional gauge theories, revealing a Fourier transform-based duality and its classical limits, with implications for integrable systems and gauge theory correspondence.

Contribution

It introduces a compact formulation of spectral duality in XXZ spin chains using Fourier transform, and proves the duality in the classical limit q→1.

Findings

Spectral duality acts as Fourier transform in the spectral parameter.

Duality reduces to XXX/Gaudin duality when q→1.

Universal difference operators relate to classical spectral curves.

Abstract

Motivated by recent progress in the study of supersymmetric gauge theories we propose a very compact formulation of spectral duality between XXZ spin chains. The action of the quantum duality is given by the Fourier transform in the spectral parameter. We investigate the duality in various limits and, in particular, prove it for q-->1, i.e. when it reduces to the XXX/Gaudin duality. We also show that the universal difference operators are given by the normal ordering of the classical spectral curves.