Abstract
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, m3/2≪Mstring. 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, m3/2≃Mstring. The vacuum energy decreases monotonically and converges exponentially to zero, when m3/2 varies from Mstring 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.
Highlights
Introduction and summaryString theory unifies gravitational and gauge interactions at the quantum level
In order to show th√at the 1-loop effective potential of the sss-model can be exponentially suppressed, O(Ms4 e−c Im T1 ), when the supersymmetry breaking scale is low, we look for conditions such that the massless fermions and bosons present in the regime Im T1 1, U1 = O(i) satisfy nF = nB [12]
The contribution of the effective potential arising for n1 = n2 = 0 grows linearly with the dual volume (2π )2Im T1/(2Ms2). This behavior is drastically different to that encountered in Regime (I), where the potential is exponentially suppressed in Im T1 (or scales likem43/2 if nF = nB) and vanishes in the limit where N = 4 supersymmetry is restored
Summary
String theory unifies gravitational and gauge interactions at the quantum level. To describe particle physics, one can naturally consider classical models defined in four-dimensional. The gaugino condensation breaking mechanism leads naturally to a small gravitino mass, even though the moduli fields Im zi ’s are of order 1 This non-perturbative scenario can only be studied qualitatively at the effective supergravity level, since no fully quantitative derivation from string computations is available yet. Note that the stability of the super no-scale models is always guaranteed when they are considered at finite temperature T , as long as T is greater than m3/2 This follows from the fact that in the effective potential at finite temperature – the quantum free energy –, all squared masses are shifted by T 2, which implies that all moduli deformations are stabilized at YIJ = 0 [23].
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