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We solve for the effective actions on the Coulomb branches of a class of N=2supersymmetric theories by finding the complex structure of an M5 brane in anappropriate background hyperkahler geometry corresponding to the lift of twoO6^- orientifolds and four D6 branes to M theory. The resulting Seiberg-Wittencurves are of finite genus, unlike other solutions proposed in the literature.The simplest theories in this class are the scale invariant Sp(k) theory withone antisymmetric and four fundamental hypermultiplets and the SU(k) theorywith two antisymmetric and four fundamental hypermultiplets. Infinite classesof related theories are obtained by adding extra SU(k) factors withbifundamental matter and by turning on masses to flow down to variousasymptotically free theories. The N=4 supersymmetric SU(k) theory can beembedded in these asymptotically free theories, allowing a derivation of asubgroup of its S duality group as an exact equivalence of quantum fieldtheories.Comment: 45 pages, 3 figures. Reference adde

The M theory lift of two O6−planes and four D6 branes

The M theory lift of two O6⁻planes and four D6 branes