Gravitational threshold corrections in non-supersymmetric heterotic strings

We compute one-loop quantum corrections to gravitational couplings in the effective action of four-dimensional heterotic strings where supersymmetry is spontaneously broken by Scherk-Schwarz fluxes. We show that in both heterotic and type II theories of this class, no moduli dependent corrections to the Planck mass are generated. We explicitly compute the one-loop corrections to the R2 coupling and find that, despite the absence of supersymmetry, its contributions may still be organised into representations of subgroups of the modular group, and admit a universal form, determined uniquely by the multiplicities of the ground states of the theory. Moreover, similarly to the case of gauge couplings, also the gravitational sector may become strongly coupled in models which dynamically induce large volume for the extra dimensions.