Instanton calculus and nonperturbative relations in N = 2 supersymmetric gauge theories

Using instanton calculus we check, in the weak coupling region, the nonperturbative relation {l_angle}Tr{phi}{sup 2}{r_angle}=i{pi}[ F{minus}(a/2){partial_derivative}{partial_derivative}a] obtained for a N=2 globally supersymmetric gauge theory. Our computations are performed for instantons of winding number k, up to k=2, and turn out to agree with previous nonperturbative results. {copyright} {ital 1997} {ital The American Physical Society}