New S - Dualities in N = 2 Supersymmetric SU ( 2 ) x SU ( 2 ) Gauge Theory

New S-dualities in a scale invariant N = 2 gauge theory with SU(2) × 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 Mand 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.