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

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 $\mathcal{N}=2$ 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.

LaTeX, 9 pages, various changes and generalisations (in particular in Section 4)

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