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 ∼ 10 16 GeV, offering an appealing scenario for unification of grav-itational 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.