  New S-dualities in a scale invariant N=2 gauge theory with SU(2) x SU(2)
gauge group are derived from embeddings of the theory in two different larger
asymptotically free theories. The true coupling space of the scale invariant
theory is a 20-fold identification of the coupling space found in the M- and
string-theory derivations of the low energy effective action, implying a larger
S-duality group. Also, this coupling space is different from the naively
expected direct product of two SL(2,Z) fundamental domains, as it contains a
different topology of fixed points.
