Large radii and string unification

We study strong coupling effects in four-dimensional heterotic string models where supersymmetry is spontaneously broken with large internal dimensions, consistently with perturbative unification of gauge couplings. These effects give rise to thresholds associated to the dual theories: type I superstring or M-theory. In the case of one large dimension, we find that these thresholds appear close to the field-theoretical unification scale ∼ 1016 GeV, offering an appealing scenario for unification of gravitational and gauge interactions. We also identify the inverse size of the eleventh dimension of M-theory with the energy at which four-fermion effective operators become important.