Locally stable non-supersymmetric Minkowski vacua in supergravity

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 Kähler 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 Kähler 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.

D 3 ¯ $$ \overline{D3} $$ induced geometric inflation

“…For these models it was more useful to employ the Kähler potential and the superpotential W since the Kähler function G has a singularity at W = 0. Meanwhile, the analysis of non-supersymmetric Minkowski and metastable de Sitter vacua with spontaneously broken supersymmetry was based mostly on the analysis using the Kähler function G, see for example, [33][34][35][36][37]. Comparative to this analysis, the new ingredient here is the fact that the S superfield is nilpotent and that we will use it for developing inflationary models with the exit to de Sitter minima.…”

Model independent limits on an ultralight gravitino from supernovae

“…In fact, even if the sgoldstino direction is univocally determined by the SUSY breaking direction in the scalar field space, the scalar mass matrix is often non-diagonal and the sgoldstinos in general mix with the other moduli fields, so that they are not in general eigenstates of the scalar mass matrix (see e.g. [51][52][53] for constraints arising from the scalar mass matrix in Minkowski and de-Sitter vacua). We will consider the Lagrangian given above to include in an effective way the presence also of those additional scalars.…”

A local evaluation of global issues in SUSY breaking

“…The sGoldstino is its complex scalar partner which therefore has averaged squared mass (half the trace of the squared mass matrix, [9] (when V | 0 = 0)…”