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Moduli (Dilaton, Volume and Shape) Stabilization via Massless F and D String Modes

Subodh P. Patil

TL;DR

This paper tackles the moduli stabilization problem in string theory by extending string gas cosmology to stabilize the dilaton together with volume and shape moduli using a gas of massless string modes. By working within the low-energy dilaton-gravity framework and focusing on toroidal compactifications, the authors show that massless F-string modes can stabilize the radii around the self-dual point, and that with dilaton stabilization this mechanism can also fix the dilaton itself. A key challenge is a zero mode that arises in the coupled dilaton-radion dynamics, which the authors address by introducing a gas of D-strings; at a special weak-coupling point where D- and F-string tensions are matched, all moduli stabilize with positive Hessian eigenvalues. The results suggest a robust, phenomenologically viable moduli stabilization scenario without fine-tuning, with testable predictions linked to the string coupling and the presence of a pervasive string gas in the present universe, while also acknowledging limitations regarding manifolds without 1-cycles and the potential need to incorporate fluxes or branes for broader applicability.

Abstract

Finding a consistent way to stabilize the various moduli fields which generically appear in string theory compactifications, is essential if string theory is to make contact with the physics we see around us. We present, in this paper, a mechanism to stabilize the dilaton within a framework that has already proven itself capable of stabilizing the volume and shape moduli of extra dimensions, namely string gas cosmology. Building on previous work, which uncovered the special role played by massless F-string modes in stabilizing extra dimensions once the dilaton has stabilized, we find that the string gas cosmology of such modes also offers a consistent mechanism to stabilize the dilaton itself, given the stabilization of the extra dimensions. We then generalize the model to include D-string gases, and find that in the case of bosonic string theory, it is possible to simultaneously stabilize all the moduli we consider consistent with weak coupling. We find that our stabilization mechanism is robust, phenomenologically consistent and evades certain difficulties which might previously have seemed to generically plague moduli stabilization mechanisms, without the need for any fine tuning.

Moduli (Dilaton, Volume and Shape) Stabilization via Massless F and D String Modes

TL;DR

This paper tackles the moduli stabilization problem in string theory by extending string gas cosmology to stabilize the dilaton together with volume and shape moduli using a gas of massless string modes. By working within the low-energy dilaton-gravity framework and focusing on toroidal compactifications, the authors show that massless F-string modes can stabilize the radii around the self-dual point, and that with dilaton stabilization this mechanism can also fix the dilaton itself. A key challenge is a zero mode that arises in the coupled dilaton-radion dynamics, which the authors address by introducing a gas of D-strings; at a special weak-coupling point where D- and F-string tensions are matched, all moduli stabilize with positive Hessian eigenvalues. The results suggest a robust, phenomenologically viable moduli stabilization scenario without fine-tuning, with testable predictions linked to the string coupling and the presence of a pervasive string gas in the present universe, while also acknowledging limitations regarding manifolds without 1-cycles and the potential need to incorporate fluxes or branes for broader applicability.

Abstract

Finding a consistent way to stabilize the various moduli fields which generically appear in string theory compactifications, is essential if string theory is to make contact with the physics we see around us. We present, in this paper, a mechanism to stabilize the dilaton within a framework that has already proven itself capable of stabilizing the volume and shape moduli of extra dimensions, namely string gas cosmology. Building on previous work, which uncovered the special role played by massless F-string modes in stabilizing extra dimensions once the dilaton has stabilized, we find that the string gas cosmology of such modes also offers a consistent mechanism to stabilize the dilaton itself, given the stabilization of the extra dimensions. We then generalize the model to include D-string gases, and find that in the case of bosonic string theory, it is possible to simultaneously stabilize all the moduli we consider consistent with weak coupling. We find that our stabilization mechanism is robust, phenomenologically consistent and evades certain difficulties which might previously have seemed to generically plague moduli stabilization mechanisms, without the need for any fine tuning.

Paper Structure

This paper contains 13 sections, 143 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Case For Massless String Modes
  3. Outlook, Outline and Conventions
  4. The Model
  5. Fixed Dilaton
  6. Fixed Radii
  7. Coupled Dilaton-Radion Dynamics
  8. D-strings
  9. Shape Stabilization, Consistency Checks and Summary
  10. Conclusions and Outlook
  11. Acknowledgements
  12. The Energy Momentum Tensor
  13. Summation Over Massless Modes

Figures (2)

  • Figure 1: Potential generated generated for the volume modulus ($V = (b/\alpha')^p$) in units of $\frac{8\pi G_d \mu_0}{\sqrt{g_s}}$ v.s. $b/\sqrt{\alpha'}$.
  • Figure 2: Potential generated generated for $\omega$ in units of $\frac{16\pi G_d \mu_0p(8p-4)}{(D-1)\alpha'\sqrt{g_s}|p_d|}$ v.s. $\omega$.