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

TL;DR

This paper calculates gravitational couplings in string theories, linking instanton effects from fivebranes in heterotic string theory to dual descriptions in type IIA string theory on compact manifolds.

Contribution

It provides a detailed computation of $F_1$ couplings and relates fivebrane instanton effects to gravitational couplings in dual string theories.

Findings

Derived the gravitational coupling $F_1$ for IIA on $K3 imes T^2$

Mapped heterotic fivebrane instanton effects to gravitational couplings

Identified fivebranes as zero size instantons in heterotic theory

Abstract

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.