Instanton Calculus and Nonperturbative Relations in N=2 Supersymmetric Gauge Theories

Abstract

Using instanton calculus we check, in the weak coupling region, the nonperturbative relation $$ <\Trϕ^2>=iπ\left(\cf-{a\over 2} {\partial\cf\over\partial a}\right)$$ 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.