  We solve for the effective actions on the Coulomb branches of a class of N=2
supersymmetric theories by finding the complex structure of an M5 brane in an
appropriate background hyperkahler geometry corresponding to the lift of two
O6^- orientifolds and four D6 branes to M theory. The resulting Seiberg-Witten
curves are of finite genus, unlike other solutions proposed in the literature.
The simplest theories in this class are the scale invariant Sp(k) theory with
one antisymmetric and four fundamental hypermultiplets and the SU(k) theory
with two antisymmetric and four fundamental hypermultiplets. Infinite classes
of related theories are obtained by adding extra SU(k) factors with
bifundamental matter and by turning on masses to flow down to various
asymptotically free theories. The N=4 supersymmetric SU(k) theory can be
embedded in these asymptotically free theories, allowing a derivation of a
subgroup of its S duality group as an exact equivalence of quantum field
theories.
