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Moduli Redefinitions and Moduli Stabilisation

Joseph P. Conlon, Francisco G. Pedro

TL;DR

This work investigates how one-loop moduli redefinitions affect the LARGE Volume Scenario (LVS) in Type IIB string compactifications and the resulting soft SUSY breaking. By modeling a 1-loop shift in the Kähler moduli, notably \\tau_s \\to \\tau_s - \\alpha \\ln(\\mathcal{V}) and \\tau_b \\to \\tau_b - \\beta \\ln(\\mathcal{V}), the authors derive corrected Kähler potentials and scalar potentials, analyze the stabilized minima for the canonical LVS model on \\mathbb{P}^4_{[1,1,1,6,9]}, and compare analytical results with numerical minima. They find that small-modulus redefinitions do not destroy the LVS minimum, while large-modulus redefinitions can induce a runaway, potentially removing the large-volume minimum. The study extends to soft SUSY breaking, showing that redefinitions can modify soft terms and even bring them to the order of the gravitino mass, depending on the regime and matter metrics, though a fully loop-corrected Kähler potential is required for definitive statements. Overall, the results highlight the LVS’s robustness to certain loop effects but reveal a sensitivity to large-volume redefinitions and underline the need for explicit loop computations to nail down the phenomenological implications.

Abstract

Field redefinitions occur in string compactifications at the one loop level. We review arguments for why such redefinitions occur and study their effect on moduli stabilisation and supersymmetry breaking in the LARGE volume scenario. For small moduli, although the effect of such redefinitions can be larger than that of the $α'$ corrections in both the Kähler and scalar potentials, they do not alter the structure of the scalar potential. For the less well motivated case of large moduli, the redefinitions can dominate all other terms in the scalar potential. We also study the effect of redefinitions on the structure of supersymmetry breaking and soft terms.

Moduli Redefinitions and Moduli Stabilisation

TL;DR

This work investigates how one-loop moduli redefinitions affect the LARGE Volume Scenario (LVS) in Type IIB string compactifications and the resulting soft SUSY breaking. By modeling a 1-loop shift in the Kähler moduli, notably \\tau_s \\to \\tau_s - \\alpha \\ln(\\mathcal{V}) and \\tau_b \\to \\tau_b - \\beta \\ln(\\mathcal{V}), the authors derive corrected Kähler potentials and scalar potentials, analyze the stabilized minima for the canonical LVS model on \\mathbb{P}^4_{[1,1,1,6,9]}, and compare analytical results with numerical minima. They find that small-modulus redefinitions do not destroy the LVS minimum, while large-modulus redefinitions can induce a runaway, potentially removing the large-volume minimum. The study extends to soft SUSY breaking, showing that redefinitions can modify soft terms and even bring them to the order of the gravitino mass, depending on the regime and matter metrics, though a fully loop-corrected Kähler potential is required for definitive statements. Overall, the results highlight the LVS’s robustness to certain loop effects but reveal a sensitivity to large-volume redefinitions and underline the need for explicit loop computations to nail down the phenomenological implications.

Abstract

Field redefinitions occur in string compactifications at the one loop level. We review arguments for why such redefinitions occur and study their effect on moduli stabilisation and supersymmetry breaking in the LARGE volume scenario. For small moduli, although the effect of such redefinitions can be larger than that of the corrections in both the Kähler and scalar potentials, they do not alter the structure of the scalar potential. For the less well motivated case of large moduli, the redefinitions can dominate all other terms in the scalar potential. We also study the effect of redefinitions on the structure of supersymmetry breaking and soft terms.

Paper Structure

This paper contains 12 sections, 84 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The LARGE Volume Scenario
  3. 1-loop Kähler Moduli Redefinition
  4. Moduli Stabilisation
  5. Redefining $\tau_s$
  6. Redefining $\tau_b$
  7. Summary
  8. Soft SUSY Breaking
  9. Redefinition of $T_a$ modulus and implications for soft SUSY breaking terms
  10. Redefining $T_a$ in the Kähler potential
  11. Redefining $T_a$ in the matter metrics
  12. Conclusions

Figures (3)

  • Figure 1: $\tau_b$ and $\tau_s$ at the minimum as functions of $\alpha$. The dots are the analytical solutions while the crosses represent the numerical results.
  • Figure 2: $\tau_b (\alpha)$ and $\tau_s (\alpha)$: The linear expansion breaks down for higher values of $\alpha$.
  • Figure 3: $\tau_b$ and $\tau_s$ at the minimum as a function of $\beta$. The red dots are the analytical solution of Eqs. while the blue dots represent the numerical result.