Fivebrane Instantons and $R^2$ couplings in $N=4$ String Theory

We compute the gravitational coupling $F_1$ for IIA string theory on $K3 \times T^2$ and use string-string duality to deduce the corresponding term for heterotic string on $T^6$. The latter is an infinite sum of gravitational instanton effects which we associate with the effects of Euclidean fivebranes wrapped on $T^6$. These fivebranes are the neutral fivebranes or zero size instantons of heterotic string theory.

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