Locally stable non-supersymmetric Minkowski vacua in supergravity

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  • 23 February 2006
Abstract
We perform a general study about the existence of non-supersymmetric minima with vanishing cosmological constant in supergravity models involving only chiral superfields. We study the conditions under which the matrix of second derivatives of the scalar potential is positive definite, and show that there exist very simple and strong necessary conditions for stability. We then derive the implications of these constraints in the case where the Kahler potential for the supersymmetry-breaking fields is separable into a sum of terms for each of the fields. We find that the resulting conditions constrain the Kahler curvature scalars and the ratios of the supersymmetry-breaking auxiliary fields defining the Goldstino direction. We also discuss the implications of our general results on the dynamics of moduli fields arising in string compactifications and on the relative sizes of their auxiliary fields, which are relevant for the soft terms of matter fields. We finally comment on how the idea of uplifting a supersymmetric AdS vacuum fits into our general study.

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