Mirror symmetry and Exact Solution of 4D N=2 Gauge Theories I
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 bifundamental 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 bifundamental matter chosen according to ADE or affine ADE Dynkin diagrams. Many of the results can be derived in an elementary way using the selfmirror 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.
 Publication:

arXiv eprints
 Pub Date:
 June 1997
 arXiv:
 arXiv:hepth/9706110
 Bibcode:
 1997hep.th....6110K
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Algebraic Geometry
 EPrint:
 62 pages, harvmac.tex (b), references added, typos corrected