Locally stable non-supersymmetric Minkowski vacua in supergravity

TL;DR

This paper investigates the conditions for stable, non-supersymmetric Minkowski vacua with zero cosmological constant in supergravity models, focusing on stability criteria and implications for string compactifications.

Contribution

It derives necessary conditions for stability based on Kahler curvature and auxiliary field ratios, providing insights into moduli dynamics and vacuum uplifting in supergravity.

Findings

Identifies strong conditions for stability related to Kahler curvature.

Shows implications for moduli stabilization in string theory.

Analyzes the role of auxiliary fields in vacuum structure.

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. We show that there exist very simple and strong necessary conditions for stability that constrain the Kahler curvature and the ratios of the supersymmetry-breaking auxiliary fields defining the Goldstino direction. We then derive more explicitly 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 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.