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Perturbative moduli stabilisation in type IIB/F-theory framework

Ignatios Antoniadis, Yifan Chen, George K. Leontaris

TL;DR

The paper addresses moduli stabilization in type IIB/F-theory compactifications, proposing a perturbative mechanism that avoids non-perturbative superpotential terms. By combining logarithmic loop corrections to the Kähler potential arising in the large two-dimensional transverse volume of intersecting D7-branes with D-term uplifts from magnetised D7-branes, it stabilises the Kähler moduli and achieves a de Sitter vacuum with broken supersymmetry. A single D7-brane can fix the transverse direction, but three intersecting D7-branes are needed to stabilise the total volume, with D-terms fixing the ratio moduli; this yields a viable dS minimum without anti-D3 uplifting or non-perturbative effects. The mechanism leverages the natural F-theory setting of intersecting 7-branes and offers a perturbative pathway to realistic vacua in string compactifications.

Abstract

We propose a new mechanism of (geometric) moduli stabilisation in type IIB/F-theory four-dimensional compactifications on Calabi-Yau manifolds, in the presence of 7-branes, that does not rely on non-perturbative effects. Complex structure moduli and the axion-dilaton system are stabilised in the standard way, without breaking supersymmetry, using 3-form internal fluxes. Kähler class moduli stabilisation utilises perturbative string loop corrections, together with internal magnetic fields along the D7-branes world-volume leading to Fayet-Iliopoulos D-terms in the effective supergravity action. The main ingredient that makes the stabilisation possible at a de Sitter vacuum is the logarithmic dependence of the string loop corrections in the large two-dimensional transverse volume limit of the 7-branes.

Perturbative moduli stabilisation in type IIB/F-theory framework

TL;DR

The paper addresses moduli stabilization in type IIB/F-theory compactifications, proposing a perturbative mechanism that avoids non-perturbative superpotential terms. By combining logarithmic loop corrections to the Kähler potential arising in the large two-dimensional transverse volume of intersecting D7-branes with D-term uplifts from magnetised D7-branes, it stabilises the Kähler moduli and achieves a de Sitter vacuum with broken supersymmetry. A single D7-brane can fix the transverse direction, but three intersecting D7-branes are needed to stabilise the total volume, with D-terms fixing the ratio moduli; this yields a viable dS minimum without anti-D3 uplifting or non-perturbative effects. The mechanism leverages the natural F-theory setting of intersecting 7-branes and offers a perturbative pathway to realistic vacua in string compactifications.

Abstract

We propose a new mechanism of (geometric) moduli stabilisation in type IIB/F-theory four-dimensional compactifications on Calabi-Yau manifolds, in the presence of 7-branes, that does not rely on non-perturbative effects. Complex structure moduli and the axion-dilaton system are stabilised in the standard way, without breaking supersymmetry, using 3-form internal fluxes. Kähler class moduli stabilisation utilises perturbative string loop corrections, together with internal magnetic fields along the D7-branes world-volume leading to Fayet-Iliopoulos D-terms in the effective supergravity action. The main ingredient that makes the stabilisation possible at a de Sitter vacuum is the logarithmic dependence of the string loop corrections in the large two-dimensional transverse volume limit of the 7-branes.

Paper Structure

This paper contains 9 sections, 49 equations, 2 figures.

Table of Contents

  1. Introduction
  2. General Overview
  3. Effective supergravity, dualities and quantum corrections
  4. D-terms in the presence of $D7$-branes
  5. Volume Stabilisation from Intersecting $D7$-Branes
  6. A Single $D7$-Brane
  7. Stabilisation of the total volume by three intersecting $D7$-branes
  8. D-term uplifting and ratios stabilisation
  9. Conclusions

Figures (2)

  • Figure 1: The scalar potential of eq. (\ref{['Ftermpotential']}) for the choice $\mathcal{W}_0$ = 1.
  • Figure 2: Sum of the F- and D-term contributions to the potential (\ref{['Ftermpotential']}) and (\ref{['VD-term']}) in terms of $\textrm{ln}({\mathcal{V}})$ and $\textrm{ln} (\tau_3)$ with the choice $\mathcal{W}_0$ = 1, $\eta_\tau = -0.4,\, d_1 = d_2 = 0.00375$, $d_3 = 0.0018$. The blue area corresponds to $V = 10^{-8}$ plane.