Separation of Variables and Vacuum Structure of N=2 SUSY QCD

TL;DR

This paper demonstrates how separation of variables can be used to construct integrable models that describe the vacuum structure of four-dimensional N=2 SUSY Yang-Mills theories, including generalizations of known integrable systems.

Contribution

It introduces a method to connect separation of variables with the construction of integrable models for N=2 SUSY QCD, extending known models to new gauge groups and matter content.

Findings

Constructed integrable models for SU(N) with N_f<2N matter hypermultiplets.

Generalized the periodic Toda lattice for these theories.

Linked special cases of massive SU(3) gauge theory to generalized Goryachev-Chaplygin tops.

Abstract

We show how the method of separation of variables can be used to construct integrable models corresponding to curves describing vacuum structure of four-dimensional ${\cal N} = 2$ SUSY Yang-Mills theories. We use this technique to construct models corresponding to $SU(N)$ Yang-Mills theory with $N_f<2N$ matter hypermultiplets by generalising the periodic Toda lattice. We also show that some special cases of massive $SU(3)$ gauge theory can be equivalently described by the generalisations of the Goryachev-Chaplygin top obtained via separation of variables.