INSTANTONS AND RECURSION-RELATIONS IN N=2 SUSY GAUGE-THEORY

We find the transformation properties of the prepotential F of N = 2 S USY gauge theory with gauge group SU(2). Next we show that G(a) = pi i (F(a) -1/2 ad(a)F(a)) is modular invariant. We also show that u = G(a ), so that F([phi]) = 1/pi i [tr phi(2)] + 1/2[phi][phi D]. This impli es that G(a) satisfies the non-linear differential equation (1-G(2)) G '' + 1/4aG('3) = 0. We use this equation to derive recursion relation s for the instanton contributions. These results can be extended to mo re general cases.