Integrable Structure in SUSY Gauge Theories, and String Duality

Details Integrable Structure in SUSY Gauge Theories, and String Duality Integrable Structure in SUSY Gauge Theories, and String Duality

1996-07-29

arxiv.org/abs/hep-th/9607223v1

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, RevTeX, Talks given at the Inauguration Conference of APCTP, June 4-10, 1996, Seoul, Korea, and at the Argonne Duali

Scientific paper

There is a close relation between duality in $N=2$ SUSY gauge theories and integrable models. In particular, the quantum moduli space of vacua of $N=2$ SUSY $SU(3)$ gauge theories coupled to two flavors of massless quarks in the fundamental representation can be related to the spectral curve of the Goryachev-Chaplygin top. Generalizing this to the cases with {\it massive} quarks, and $N_f = 0,1,2$, we find a corresponding integrable system in seven dimensional phase space where a hyperelliptic curve appears in the Painlev\'e test. To understand the stringy origin of the integrability of these theories we obtain exact nonperturbative point particle limit of type II string compactified on a Calabi-Yau manifold, which gives the hyperelliptic curve of $SU(2)$ QCD with $N_f =1$ hypermultiplet.

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