Integrable Structure in SUSY Gauge Theories, and String Duality
Abstract
Description
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 Painlevé 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.
10 pages, RevTeX, Talks given at the Inauguration Conference of APCTP, June 4-10, 1996, Seoul, Korea, and at the Argonne Duality Institute, June 27-July 12, 1996, Argonne Nat. Lab., USA
10 pages, RevTeX, Talks given at the Inauguration Conference of APCTP, June 4-10, 1996, Seoul, Korea, and at the Argonne Duality Institute, June 27-July 12, 1996, Argonne Nat. Lab., USA