Mass formulae and natural hierarchy in string effective supergravities

Abstract

We study some conditions for the hierarchy $m_{3/2}<<M_P$ to occur naturally in a generic effective supergravity theory. Absence of fine-tuning and perturbative calculability require that the effective potential has a sliding gravitino mass and vanishing cosmological constant, up to $\mathcal{O}(m_{3/2}^4)$ corrections. In particular, cancellation of quadratically divergent contributions to the one-loop effective potential should take place, including the `hidden sector' of the theory. We show that these conditions can be met in the effective supergravities derived from four-dimensional superstrings, with supersymmetry broken either at the string tree level via compactification, or by non-perturbative effects such as gaugino condensation. A crucial role is played by some approximate scaling symmetries, which are remnants of discrete target-space dualities in the large moduli limit. We derive explicit formulae for the soft breaking terms arising from this class of `large hierarchy compatible' (LHC) supergravities.

40 pages, no figures, CERN-TH.7192/94, LPTENS -94/12, UCLA/94/TEP13 (plain LATEX, to be run twice). Some trivial misprints and references have been corrected

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