The heterotic prepotential from eleven dimensions

We compactify M-theory in the Horava-Witten formulation on S^1/Z_2 \times K3 \times T^2. Focusing on the moduli-space of vector multiplets of the resulting four-dimensional N=2 theory, we determine the prepotential as an expansion in two dimensionless parameters which both scale as \kappa^{2/3}. We determine the prepotential completely to relative order \kappa^{4/3} and compare the expression with the results obtained for the perturbative string theories. We find complete agreement to relative order \kappa^{4/3} between the strong and weak coupling regimes. The sources of higher order perturbative and non-perturbative corrections to the prepotential are also briefly discussed from the M-theory perspective.