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General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation

Michele Cicoli, Joseph P. Conlon, Fernando Quevedo

TL;DR

The paper probes the conditions under which type IIB flux compactifications yield exponentially large volume vacua (LVS). It shows that a negative Euler characteristic and at least one blow-up mode resolving a point-like singularity are necessary and sufficient for LVS, with string-loop corrections crucial for stabilizing directions transverse to the overall volume, especially in fibration Calabi–Yau manifolds. By analyzing several explicit Calabi–Yau examples (Swiss cheese and K3-fibered), the authors demonstrate how loop effects can lift flat directions and even stabilise cycles hosting Standard Model sectors. The work highlights the interplay between $oldsymbol{}$ corrections, nonperturbative effects, and $oldsymbol{g_s}$ corrections, and discusses potential phenomenological and cosmological implications such as modular inflation and dark-sector scenarios within LVS.

Abstract

We study the topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. We show that negative Euler number and the existence of at least one blow-up mode resolving point-like singularities are necessary and sufficient conditions for moduli stabilisation with exponentially large volumes. We also analyse the general effects of string loop corrections on this scenario. While the combination of alpha' and nonperturbative corrections are sufficient to stabilise blow-up modes and the overall volume, quantum corrections are needed to stabilise other directions transverse to the overall volume. This allows exponentially large volume minima to be realised for fibration Calabi-Yaus, with the various moduli of the fibration all being stabilised at exponentially large values. String loop corrections may also play a role in stabilising 4-cycles which support chiral matter and cannot enter directly into the non-perturbative superpotential. We illustrate these ideas by studying the scalar potential for various Calabi-Yau three-folds including K3 fibrations and briefly discuss the potential phenomenological and cosmological implications of our results.

General Analysis of LARGE Volume Scenarios with String Loop Moduli Stabilisation

TL;DR

The paper probes the conditions under which type IIB flux compactifications yield exponentially large volume vacua (LVS). It shows that a negative Euler characteristic and at least one blow-up mode resolving a point-like singularity are necessary and sufficient for LVS, with string-loop corrections crucial for stabilizing directions transverse to the overall volume, especially in fibration Calabi–Yau manifolds. By analyzing several explicit Calabi–Yau examples (Swiss cheese and K3-fibered), the authors demonstrate how loop effects can lift flat directions and even stabilise cycles hosting Standard Model sectors. The work highlights the interplay between corrections, nonperturbative effects, and corrections, and discusses potential phenomenological and cosmological implications such as modular inflation and dark-sector scenarios within LVS.

Abstract

We study the topological conditions for general Calabi-Yaus to get a non-supersymmetric AdS exponentially large volume minimum of the scalar potential in flux compactifications of IIB string theory. We show that negative Euler number and the existence of at least one blow-up mode resolving point-like singularities are necessary and sufficient conditions for moduli stabilisation with exponentially large volumes. We also analyse the general effects of string loop corrections on this scenario. While the combination of alpha' and nonperturbative corrections are sufficient to stabilise blow-up modes and the overall volume, quantum corrections are needed to stabilise other directions transverse to the overall volume. This allows exponentially large volume minima to be realised for fibration Calabi-Yaus, with the various moduli of the fibration all being stabilised at exponentially large values. String loop corrections may also play a role in stabilising 4-cycles which support chiral matter and cannot enter directly into the non-perturbative superpotential. We illustrate these ideas by studying the scalar potential for various Calabi-Yau three-folds including K3 fibrations and briefly discuss the potential phenomenological and cosmological implications of our results.

Paper Structure

This paper contains 25 sections, 239 equations, 6 figures.

Table of Contents

  1. Introduction
  2. The LARGE Volume Scenario
  3. Low Energy Limit for Type IIB Flux Compactifications
  4. General Analysis for the Large Volume Limit
  5. Particular Examples
  6. The single-hole Swiss cheese: $\mathbb{C}P_{[1,1,1,6,9]}^{4}$
  7. The multiple-hole Swiss cheese: $\mathcal{F}_{11}$ and $\mathbb{C}P_{[1,3,3,3,5]}^{4}$
  8. 2-Parameter K3 Fibration: $\mathbb{C}P_{[1,1,2,2,6]}^{4}$
  9. Explicit Calculation
  10. 3-Parameter K3 Fibration
  11. Explicit Calculation
  12. Inclusion of the String Loop Corrections
  13. LARGE Volume and String Loop Corrections
  14. Moduli Stabilisation via String Loop Corrections
  15. The single-hole Swiss cheese: $\mathbb{C}P_{[1,1,1,6,9]}^{4}$
  16. ...and 10 more sections

Figures (6)

  • Figure 1: Change of coordinates of the Kähler moduli space.
  • Figure 2: "Sofa" potential with the presence of a flat direction.
  • Figure 3: $\tau_{SM}$ fixed by string loop corrections. The numerical values used are $\lambda_{1}=\lambda_{2}=1$, $\lambda_{3}=50$, $\lambda_{4}=\lambda_{5}=5$ and then we have fixed $\tau_{E3}=10$ and $\mathcal{V}=\sqrt{10}e^{20\pi}$.
  • Figure 4: $V$ versus $\Omega$ at $\mathcal{V}$ and $\tau_{3}$ fixed.
  • Figure 5: Blow-up cycle $\tau_{1}$ resolving a point-like singularity.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Claim 1
  • Claim 2
  • Claim 3
  • Claim 4
  • Claim 5
  • Claim 6