Five-brane instantons and R**2 couplings in N=4 string theory

We compute the gravitational coupling F{sub 1} for type IIA string theory on K3{times}T{sup 2} and use string-string duality to deduce the corresponding term for heterotic string on T{sup 6}. The latter is an infinite sum of gravitational instanton effects which we associate with the effects of Euclidean five-branes wrapped on T{sup 6}. These five-branes are the neutral five-branes or zero-size instantons of heterotic string theory. {copyright} {ital 1998} {ital The American Physical Society}