Three-Generation Super No-Scale Models in Heterotic Superstrings

We derive the conditions for the one-loop contribution to the cosmological constant to be exponentially suppressed in a class of heterotic string compactifications with three generations of chiral matter, where supersymmetry is spontaneously broken à la Scherk-Schwarz. Using techniques of partial unfolding based on the Hecke congruence subgroup ${\mathrm{\Gamma }}_0(2)$ of the modular group to extract the leading asymptotics, we show that the super no-scale condition $n_B=n_F$ between the degeneracies of massless bosons $n_B$ and fermions $n_F$ in the full string spectrum is necessary but not sufficient, and needs to be supplemented by additional conditions which we identify. We use these results to construct three-generation Pati-Salam models with interesting phenomenological characteristics.