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Metastable SUSY Breaking, de Sitter Moduli Stabilisation and Kähler Moduli Inflation

Sven Krippendorf, Fernando Quevedo

TL;DR

The paper shows that anomalous U(1) D-terms can provide a fully supersymmetric uplifting mechanism in IIB string compactifications, transforming a runaway ISS potential with one Kähler modulus into a stable, large-volume minimum when a second modulus is present. It demonstrates LVS-like moduli stabilization with D-term uplift to de Sitter space, yielding SUSY breaking of ISS type and flavor-universal soft terms, while remaining compatible with known metastability constraints. It further shows that Kähler moduli inflation and fibre inflation can be embedded in this uplifted, fully supersymmetric framework, avoiding non-SUSY uplifting terms. The results suggest a broadly applicable mechanism for achieving dS vacua and inflation in string theory, with potential implications for phenomenology and model-building in LVS-like setups.

Abstract

We study the influence of anomalous U(1) symmetries and their associated D-terms on the vacuum structure of global field theories once they are coupled to N=1 supergravity and in the context of string compactifications with moduli stabilisation. In particular, we focus on a IIB string motivated construction of the ISS scenario and examine the influence of one additional U(1) symmetry on the vacuum structure. We point out that in the simplest one-Kahler modulus compactification, the original ISS vacuum gets generically destabilised by a runaway behaviour of the potential in the modulus direction. In more general compactifications with several Kahler moduli, we find a novel realisation of the LARGE volume scenario with D-term uplifting to de Sitter space and both D-term and F-term supersymmetry breaking. The structure of soft supersymmetry breaking terms is determined in the preferred scenario where the standard model cycle is not stabilised non-perturbatively and found to be flavour universal. Our scenario also provides a purely supersymmetric realisation of Kahler moduli (blow-up and fibre) inflation, with similar observational properties as the original proposals but without the need to include an extra (non-SUSY) uplifting term.

Metastable SUSY Breaking, de Sitter Moduli Stabilisation and Kähler Moduli Inflation

TL;DR

The paper shows that anomalous U(1) D-terms can provide a fully supersymmetric uplifting mechanism in IIB string compactifications, transforming a runaway ISS potential with one Kähler modulus into a stable, large-volume minimum when a second modulus is present. It demonstrates LVS-like moduli stabilization with D-term uplift to de Sitter space, yielding SUSY breaking of ISS type and flavor-universal soft terms, while remaining compatible with known metastability constraints. It further shows that Kähler moduli inflation and fibre inflation can be embedded in this uplifted, fully supersymmetric framework, avoiding non-SUSY uplifting terms. The results suggest a broadly applicable mechanism for achieving dS vacua and inflation in string theory, with potential implications for phenomenology and model-building in LVS-like setups.

Abstract

We study the influence of anomalous U(1) symmetries and their associated D-terms on the vacuum structure of global field theories once they are coupled to N=1 supergravity and in the context of string compactifications with moduli stabilisation. In particular, we focus on a IIB string motivated construction of the ISS scenario and examine the influence of one additional U(1) symmetry on the vacuum structure. We point out that in the simplest one-Kahler modulus compactification, the original ISS vacuum gets generically destabilised by a runaway behaviour of the potential in the modulus direction. In more general compactifications with several Kahler moduli, we find a novel realisation of the LARGE volume scenario with D-term uplifting to de Sitter space and both D-term and F-term supersymmetry breaking. The structure of soft supersymmetry breaking terms is determined in the preferred scenario where the standard model cycle is not stabilised non-perturbatively and found to be flavour universal. Our scenario also provides a purely supersymmetric realisation of Kahler moduli (blow-up and fibre) inflation, with similar observational properties as the original proposals but without the need to include an extra (non-SUSY) uplifting term.

Paper Structure

This paper contains 20 sections, 102 equations, 8 figures, 2 tables.

Table of Contents

  1. Introduction
  2. The ISS model and its embedding into String Theory
  3. The One-modulus Case
  4. The Two-moduli Case
  5. Strategy
  6. Matter field stabilisation
  7. Stabilising the Kähler moduli
  8. D7 Soft-Terms
  9. Kähler moduli inflation
  10. 3-Parameter K3 fibration and Fibre Inflation
  11. Fibre Inflation
  12. Constraints for metastable dS vacua in supergravity setups
  13. Constraints on Anomalous $U(1)$ Gauge Symmetries as Uplifting Potential
  14. Conclusions
  15. On stabilising the F-term potential with a constraint
  16. ...and 5 more sections

Figures (8)

  • Figure 1: This plot shows the F-term potential in dependence of the Kähler modulus $\tau$ and the remaining matter degree of freedom $\Phi.$ We display small values of $\Phi$ in order to show the reader the runaway behaviour, which is clearly shown in the picture. Keeping $\Phi$ constant would give the typical KKLT situation.
  • Figure 2: A plot of the numerical behaviour of the scalar potential with respect to the Kähler moduli showing an AdS minimum.
  • Figure 3: A plot of the numerical behaviour of the scalar potential with respect to the Kähler moduli showing a dS minimum.
  • Figure 4: A plot of the numerical behaviour of the scalar potential with respect to the Kähler moduli showing no minimum.
  • Figure 5: A plot of the numerical behaviour of the scalar potential with respect to the Kähler moduli with a minimum of $V=5.74\times 10^{-26}.$
  • ...and 3 more figures