Abstract

We investigate de Sitter solutions of mathcal{N}=1 supergravity with an F-term scalar potential near a no-scale Minkowski point, as they may in particular arise from flux compactifications in string theory. We show that a large class of such solutions has a universal tachyon with eta le -frac{4}{3} at positive vacuum energies, thus forbidding meta-stable de Sitter vacua and slow-roll inflation. The tachyon aligns with the sgoldstino in the Minkowski limit, whereas the sgoldstino itself is generically stable in the de Sitter vacuum due to mass mixing effects. We specify necessary conditions for the superpotential and the Kähler potential to avoid the instability. Our result may also help to explain why the program of classical de Sitter hunting has remained unsuccessful, while constructions involving instantons or non-geometric fluxes have led to various examples of meta-stable de Sitter vacua.

Highlights

  • Attempts to construct explicit meta-stable de Sitter vacua in string theory face a number of well-known theoretical and computational challenges

  • We investigate de Sitter solutions of N = 1 supergravity with an F-term scalar potential near a no-scale Minkowski point, as they may in particular arise from flux compactifications in string theory

  • Many interesting questions are related to this issue: which other mechanisms for de Sitter (dS) vacua, if any, exist in string theory? What are the minimal ingredients a compactification requires in order to admit dS vacua? Is it possible to construct simpler models than those already known, perhaps even some that are fully explicit at the 10d level? How are observables such as the cosmological constant, moduli masses or the supersymmetry breaking scale distributed across the landscape? etc

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Summary

Introduction

Attempts to construct explicit meta-stable de Sitter (dS) vacua in string theory face a number of well-known theoretical and computational challenges. Given the vast amount of possible string vacua, a promising strategy to address such questions would be to identify universal, model-independent constraints These may help to rule out cosmological solutions in whole regions of the landscape and, even more importantly, point us to interesting regions where such solutions do exist. It was conjectured in [73] that this mode is the reason why many compactifications do not admit meta-stable dS vacua even though they evade the known no-go theorems from the volume, the dilaton and the sgoldstino. It is the purpose of the present work to perform a general, model-independent analysis of this tachyon. Several longer computations are relegated to appendices A, B and C

Preliminaries
No-scale Minkowski vacua
Assumptions
A universal tachyon
Case 1
Case 2
Case 3
Evading the no-go theorem
Corrections to the Kahler potential
Non-zero Wamn
Unstabilized Φa moduli
Classical dS vacua?
Conclusions
A No-scale Minkowski solutions in string theory
B Derivation of tachyon mass
The mass
C STU model near a no-scale Minkowski point
Full Text
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