N=2 Supersymmetric QCD and Integrable Spin Chains: Rational Case N_f < 2N_c

TL;DR

This paper explores the connection between 4d N=2 supersymmetric QCD with fewer flavors than twice the number of colors and integrable spin chains, identifying the relevant spin chain model as the inhomogeneous XXX model.

Contribution

It establishes a correspondence between the spectral curve of N=2 supersymmetric QCD and inhomogeneous XXX spin chains for the case N_f < 2N_c, extending known Seiberg-Witten results.

Findings

Spectral curve matches inhomogeneous XXX spin chain for N_f < 2N_c

Identification aligns with Seiberg-Witten theory

Provides a concrete integrable model for the gauge theory

Abstract

The form of the spectral curve for $4d$ $N=2$ supersymmetric Yang-Mills theory with matter fields in the fundamental representation of the gauge group suggests that its $1d$ integrable counterpart should be looked for among (inhomogeneous) $sl(2)$ spin chains with the length of the chain being equal to the number of colours $N_c$. For $N_f < 2N_c$ the relevant spin chain is the simplest $XXX$-model, and this identification is in agreement with the known results in Seiberg-Witten theory.