Gauge and gravitational couplings from modular orbits in orbifold compactifications

We discuss the appearance of modular functions at the one-loop gauge and gravitational couplings in (0,2) non-decomposable N=1 four dimensional orbifold compactifications of the heterotic string. We define the limits for the existence of states causing singularities in the moduli space in the perturbative regime for a generic vacuum of the heterotic string. The “proof” provides evidence for the explanation of the stringy Higgs effect.