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Mirror symmetry and Exact Solution of 4D N=2 Gauge Theories I

S. Katz·P. Mayr·C. Vafa
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Abstract

Using geometric engineering in the context of type II strings, we obtain exact solutions for the moduli space of the Coulomb branch of all N=2 gauge theories in four dimensions involving products of SU gauge groups with arbitrary number of bi-fundamental matter for chosen pairs, as well as an arbitrary number of fundamental matter for each factor. Asymptotic freedom restricts the possibilities to SU groups with bi-fundamental matter chosen according to ADE or affine ADE Dynkin diagrams. Many of the results can be derived in an elementary way using the self-mirror property of K3. We find that in certain cases the solution of the Coulomb branch for N=2 gauge theories is given in terms of a three dimensional complex manifold rather than a Riemann surface. We also study new stringy strong coupling fixed points arising from the compactification of higher dimensional theories with tensionless strings and consider applications to three dimensional N=4 theories.

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S. Katz, P. Mayr, C. Vafa. 1997-06-26. Mirror symmetry and Exact Solution of 4D N=2 Gauge Theories I. https://arxiv.org/abs/hep-th/9706110

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