Three-generation super no-scale models in heterotic superstrings

We derive the conditions for one-loop contribution to cosmological constant be exponentially suppressed in a class of heterotic string compactifications with three generations chiral matter, where supersymmetry is spontaneously broken \`a la Scherk-Schwarz. Using techniques partial unfolding based on Hecke congruence subgroup $\Gamma_0(2)$ modular group extract leading asymptotics, we show that super no-scale condition $n_B=n_F$ between degeneracies massless bosons $n_B$ and fermions $n_F$ full spectrum necessary but not sufficient, needs supplemented by additional which identify. use these results construct three-generation Pati-Salam models interesting phenomenological characteristics.