Four-dimensional supergravity theories consistent with the symmetries of superstrings

We analyse four-dimensional supergravity theories obtained as the low-energy limit of heterotic superstring compactification. Using the restrictions implied by the classical symmetries on the effective action for the massless modes, we derive general properties of the scalar potential. It is found that the global positivity of the scalar potential is not guaranteed: an extra condition on the Kähler potential is required. In this case, even if supersymmetry is broken by non-perturbative effects in the hidden sector, there is no supersymmetry breaking in the observable sector at tree level. However, the existence of charged flat directions at tree level and the absence of supersymmetry breaking in the scalar sector at one-loop are artefacts of the naïve truncation to the massless sector. Modifications to the classical action that might be induced by string-loop effects are considered. The possibility of fixing dynamically the radius of the internal manifold is discussed.