Integrability, Duality and Strings

Details Integrability, Duality and Strings Integrability, Duality and Strings

1996-04-09

arxiv.org/abs/hep-th/9604043v1

Physics

High Energy Physics

High Energy Physics - Theory

43 pages, Latex, lecture notes based on a talk of C. Gomez at the "Quantum Field Theory Workshop", Aug. 1996, Bulgary

Scientific paper

In these notes evidence is presented for intepreting the moduli space of the integrable model associated to $N\!=\!2$ gauge theories with $N\!=\!4$ matter content, in terms of Calabi-Yau manifolds. We restrict to the case of gauge group $SU(2)$, which is compared with the moduli space of the Calabi-Yau manifold $WP_{11226}^{12}$ appearing in the rank three dual pair $(K^{3}\times T^{2} / WP_{11226}^{12})$. The singularity loci of both spaces are maped in a one to one way and, in the weak coupling limit, $N\!=\!2$ $SU(2)$ pure Yang-Mills is obtained in both cases by the same type of blow up. Comments on the interpretation of the strong coupling locus from the perspective of the integrable system are done.

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