Spin Chain Models with Spectral Curves from M theory

TL;DR

This paper constructs an integrable spin chain model derived from M Theory spectral curves, linking supersymmetric gauge theories to integrable systems through Hamiltonian reduction.

Contribution

It introduces a new integrable model associated with $ ext{SU}(N)$ gauge theories with antisymmetric matter, based on spectral curves from M Theory.

Findings

The model is a Hamiltonian reduction of a periodic spin chain.

It establishes a connection between supersymmetric gauge theories and integrable systems.

The model is Hamiltonian with respect to a universal symplectic form.

Abstract

We construct the integrable model corresponding to the $\N=2$ supersymmetric SU(N) gauge theory with matter in the antisymmetric representation, using the spectral curve found by Landsteiner and Lopez through M Theory. The model turns out to be the Hamiltonian reduction of a $N+2$ periodic spin chain model, which is Hamiltonian with respect to the universal symplectic form we had constructed earlier for general soliton equations in the Lax or Zakharov-Shabat representation.