Super no-scale models in string theory

We consider “super no-scale models” in the framework of the heterotic string, where the N=4,2,1→0 spontaneous breaking of supersymmetry is induced by geometrical fluxes realizing a stringy Scherk–Schwarz perturbative mechanism. Classically, these backgrounds are characterized by a boson/fermion degeneracy at the massless level, even if supersymmetry is broken. At the 1-loop level, the vacuum energy is exponentially suppressed, provided the supersymmetry breaking scale is small, m_3/2M_string. We show that the “super no-scale string models” under consideration are free of Hagedorn-like tachyonic singularities, even when the supersymmetry breaking scale is large, m_3/2≃M_string. The vacuum energy decreases monotonically and converges exponentially to zero, when m_3/2 varies from M_string to 0. We also show that all Wilson lines associated to asymptotically free gauge symmetries are dynamically stabilized by the 1-loop effective potential, while those corresponding to non-asymptotically free gauge groups lead to instabilities and condense. The Wilson lines of the conformal gauge symmetries remain massless. When stable, the stringy super no-scale models admit low energy effective actions, where decoupling gravity yields theories in flat spacetime, with softly broken supersymmetry.