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de Sitter Vacua in String Theory

Shamit Kachru, Renata Kallosh, Andrei Linde, Sandip P. Trivedi

TL;DR

The paper demonstrates a concrete, controlled pathway to metastable de Sitter vacua in type IIB string theory by freezing all moduli via flux-induced and non-perturbative effects to obtain a SUSY AdS minimum, then uplifting with warped anti-D3 branes. It analyzes the resulting dS vacua's stability against tunneling using Coleman–De Luccia and Hawking–Moss formalisms, showing lifetimes can exceed the current cosmological epoch yet remain shorter than Poincaré recurrence, thereby avoiding conceptual issues. The construction relies on a warped throat to suppress SUSY breaking and relies on discrete flux choices to tune the cosmological constant. This work lays groundwork for string cosmology models by combining flux stabilization with non-perturbative effects and controlled uplift, while noting flux discretization as a natural tuning limitation and pointing toward future cosmological model-building within this framework.

Abstract

We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of anti-D3 branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological timescale of 10^10 years. We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

de Sitter Vacua in String Theory

TL;DR

The paper demonstrates a concrete, controlled pathway to metastable de Sitter vacua in type IIB string theory by freezing all moduli via flux-induced and non-perturbative effects to obtain a SUSY AdS minimum, then uplifting with warped anti-D3 branes. It analyzes the resulting dS vacua's stability against tunneling using Coleman–De Luccia and Hawking–Moss formalisms, showing lifetimes can exceed the current cosmological epoch yet remain shorter than Poincaré recurrence, thereby avoiding conceptual issues. The construction relies on a warped throat to suppress SUSY breaking and relies on discrete flux choices to tune the cosmological constant. This work lays groundwork for string cosmology models by combining flux stabilization with non-perturbative effects and controlled uplift, while noting flux discretization as a natural tuning limitation and pointing toward future cosmological model-building within this framework.

Abstract

We outline the construction of metastable de Sitter vacua of type IIB string theory. Our starting point is highly warped IIB compactifications with nontrivial NS and RR three-form fluxes. By incorporating known corrections to the superpotential from Euclidean D-brane instantons or gaugino condensation, one can make models with all moduli fixed, yielding a supersymmetric AdS vacuum. Inclusion of a small number of anti-D3 branes in the resulting warped geometry allows one to uplift the AdS minimum and make it a metastable de Sitter ground state. The lifetime of our metastable de Sitter vacua is much greater than the cosmological timescale of 10^10 years. We also prove, under certain conditions, that the lifetime of dS space in string theory will always be shorter than the recurrence time.

Paper Structure

This paper contains 13 sections, 38 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Flux compactifications of IIB string theory, including corrections
  3. Calabi-Yau orientifolds with flux
  4. Corrections to the no-scale models
  5. Supersymmetric AdS Vacua
  6. Constructing dS vacua
  7. $\overline{D3}$ branes in ISD fluxes
  8. Uplifting AdS vacua to dS vacua
  9. How stable is the dS vacuum?
  10. General theory
  11. Thin-wall approximation
  12. "No-wall" approximation: Hawking-Moss instanton and stochastic approach to tunneling
  13. Discussion

Figures (2)

  • Figure 1: Potential (multiplied by $10^{15}$) for the case of exponential superpotential with $W_0 =- 10^{-4}$, $A=1$, $a =0.1$. There is an AdS minimum.
  • Figure 2: Potential (multiplied by $10^{15}$) for the case of exponential superpotential and including a $D\over \sigma^3$ correction with $D=3 \times 10^{-9}$ which uplifts the AdS minimum to a dS minimum.