Target-space duality, supersymmetry breaking and the stability of classical string vacua

Target-space duality symmetries are present in many static string vacua studied up to now. They are conjectured to remain unbroken even after non-perturbative string effects are taken into account. If that is the case, one can have a handle on the non-perturbative string effects by requiring explicit duality invariance of the low-energy effective lagrangian. As an explicit example we present a general discussion of the effective four-dimensional supergravity action consistent with the target-space modular symmetry SL(2,Z). The non-perturbative superpotential severely distorts the classical, four-dimensional string solutions. Specifically, it lifts the vacuum degeneracy with respect to the compactification scale and leads in general to spontaneous supersymmetry breaking with negative vacuum energy, but we also find particular solutions with vanishing cosmological constant. Charged massless matter scalars get negative (mass)² signalling an additional instability of the vacuum, further gauge symmetry breaking and the blowing up of orbifold singularities.