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Stabilizing All Kahler Moduli in Type IIB Orientifolds

Konstantin Bobkov, Volker Braun, Piyush Kumar, Stuart Raby

TL;DR

This work introduces a robust mechanism to stabilize all Kähler moduli in Type IIB orientifolds using a single non-perturbative contribution from a D3-instanton or D7-brane gaugino condensation on an ample divisor, inspired by fluxless G2 vacua in M-theory. By exploiting the ampleness of the divisor and a single linear combination of Kähler moduli, the authors show that all four- and two-cycle volumes, as well as the Calabi-Yau volume, can be fixed inside the Kähler cone, with the stabilized values controlled by the divisor volume through the radial modulus τ_D. They provide explicit one- and three-parameter Calabi–Yau orientifold examples where the stabilization reduces to a single radial degree of freedom, derive the resulting mass spectrum (heavy moduli and axions, with some axions remaining massless at this order), and demonstrate the parametric consistency of truncating to a single non-perturbative term. The paper also discusses consistency conditions for the approximation, uplift mechanisms to de Sitter, and important phenomenological consequences, including SUSY-breaking mediation and a dynamical solution to the strong CP problem, along with the prospect of a string axiverse.

Abstract

We describe a simple and robust mechanism that stabilizes all Kahler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G_2 compactifications of M-theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kahler moduli are worked out. We find that the stabilized volumes of all two- and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.

Stabilizing All Kahler Moduli in Type IIB Orientifolds

TL;DR

This work introduces a robust mechanism to stabilize all Kähler moduli in Type IIB orientifolds using a single non-perturbative contribution from a D3-instanton or D7-brane gaugino condensation on an ample divisor, inspired by fluxless G2 vacua in M-theory. By exploiting the ampleness of the divisor and a single linear combination of Kähler moduli, the authors show that all four- and two-cycle volumes, as well as the Calabi-Yau volume, can be fixed inside the Kähler cone, with the stabilized values controlled by the divisor volume through the radial modulus τ_D. They provide explicit one- and three-parameter Calabi–Yau orientifold examples where the stabilization reduces to a single radial degree of freedom, derive the resulting mass spectrum (heavy moduli and axions, with some axions remaining massless at this order), and demonstrate the parametric consistency of truncating to a single non-perturbative term. The paper also discusses consistency conditions for the approximation, uplift mechanisms to de Sitter, and important phenomenological consequences, including SUSY-breaking mediation and a dynamical solution to the strong CP problem, along with the prospect of a string axiverse.

Abstract

We describe a simple and robust mechanism that stabilizes all Kahler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G_2 compactifications of M-theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kahler moduli are worked out. We find that the stabilized volumes of all two- and four-cycles as well as the volume of the Calabi-Yau manifold are controlled by a single parameter, namely, the volume of the ample divisor. This feature would dramatically constrain any realistic models of particle physics embedded into such compactifications. Broad consequences for phenomenology are discussed, in particular the dynamical solution to the strong CP-problem within the framework.

Paper Structure

This paper contains 15 sections, 76 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Stabilizing All Kähler Moduli with a Single Non-Perturbative Contribution
  3. Contributions to the Superpotential
  4. Coordinates on the Kähler Moduli Space
  5. Minimizing the Potential
  6. Explicit Examples
  7. A Three-Parameter Model
  8. The Geometry
  9. Stabilization of Moduli
  10. Supersymmetry Breaking and a Particular Choice of Parameters
  11. Consistency Condition for the Single Condensate/Instanton Approximation
  12. Phenomenological Consequences
  13. Mediation of Supersymmetry Breaking
  14. Dynamical Solution to the Strong CP-Problem
  15. Conclusions

Figures (1)

  • Figure 1: The scalar potential in the $\tau_D$-direction for the parameter choice in eq. \ref{['eq:sample']}.