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Five-Brane Dynamics and Inflation in Heterotic M-Theory

Evgeny I. Buchbinder

TL;DR

The work demonstrates that in heterotic M-theory with multiple Kahler moduli and five-branes on non-isolated or higher-genus curves, fluxes and non-perturbative effects can stabilize all moduli in a non-supersymmetric AdS vacuum, which can be lifted to a metastable de Sitter vacuum using Fayet-Iliopoulos terms. By combining FI uplifting with the five-brane dynamics, the translational modulus of the brane can act as an inflaton, producing a viable slow-roll inflationary phase as the brane approaches the visible sector, and terminating via the appearance of new light states that trigger a small instanton transition. The post-inflationary moduli system, now including vector-bundle transition moduli, can be stabilized with a small positive cosmological constant, making the setup phenomenologically appealing. Overall, the paper generalizes previous moduli-stabilization results, provides a concrete inflationary mechanism within a strongly coupled framework, and shows how a realistic dS vacuum can emerge after cosmological evolution.

Abstract

Generic heterotic M-theory compactifications contain five-branes wrapping non-isolated genus zero or higher genus curves in a Calabi-Yau threefold. Non-perturbative superpotentials do not depend on moduli of such five-branes.We show that fluxes and non-perturbative effects can stabilize them in a non-supersymmetric AdS vacuum. We also show that these five-branes can be stabilized in a dS vacuum, if we modify the supergravity potential energy by Fayet-Iliopoulos terms. This allows us to stabilize all heterotic M-theory moduli in a dS vacuum in the most general compactification scenarios. In addition, we demonstrate that, by this modification, one can create an inflationary potential. The inflationary phase is represented by a five-brane approaching the visible brane. We give a qualitative argument how extra states becoming light, when the five-brane comes too close, can terminate inflation. Eventually, the five-brane hits the visible brane and disappears through a small instanton transition. The post-inflationary system of moduli has simpler stability properties. It can be stabilized in a dS vacuum with a small cosmological constant.

Five-Brane Dynamics and Inflation in Heterotic M-Theory

TL;DR

The work demonstrates that in heterotic M-theory with multiple Kahler moduli and five-branes on non-isolated or higher-genus curves, fluxes and non-perturbative effects can stabilize all moduli in a non-supersymmetric AdS vacuum, which can be lifted to a metastable de Sitter vacuum using Fayet-Iliopoulos terms. By combining FI uplifting with the five-brane dynamics, the translational modulus of the brane can act as an inflaton, producing a viable slow-roll inflationary phase as the brane approaches the visible sector, and terminating via the appearance of new light states that trigger a small instanton transition. The post-inflationary moduli system, now including vector-bundle transition moduli, can be stabilized with a small positive cosmological constant, making the setup phenomenologically appealing. Overall, the paper generalizes previous moduli-stabilization results, provides a concrete inflationary mechanism within a strongly coupled framework, and shows how a realistic dS vacuum can emerge after cosmological evolution.

Abstract

Generic heterotic M-theory compactifications contain five-branes wrapping non-isolated genus zero or higher genus curves in a Calabi-Yau threefold. Non-perturbative superpotentials do not depend on moduli of such five-branes.We show that fluxes and non-perturbative effects can stabilize them in a non-supersymmetric AdS vacuum. We also show that these five-branes can be stabilized in a dS vacuum, if we modify the supergravity potential energy by Fayet-Iliopoulos terms. This allows us to stabilize all heterotic M-theory moduli in a dS vacuum in the most general compactification scenarios. In addition, we demonstrate that, by this modification, one can create an inflationary potential. The inflationary phase is represented by a five-brane approaching the visible brane. We give a qualitative argument how extra states becoming light, when the five-brane comes too close, can terminate inflation. Eventually, the five-brane hits the visible brane and disappears through a small instanton transition. The post-inflationary system of moduli has simpler stability properties. It can be stabilized in a dS vacuum with a small cosmological constant.

Paper Structure

This paper contains 14 sections, 140 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Supersymmetric AdS Vacua in Models with $h^{1,1}>1$
  3. The System of Moduli
  4. Supersymmetric AdS vacua
  5. Addition of a Five-Brane and dS Vacua
  6. Effective Potential for a Five-Brane Modulus and Non-Su-per-sym-met-ric AdS Vacua
  7. Fayet-Iliopoulos Terms and dS Vacua
  8. The Five-Brane Modulus as an Inflaton
  9. Constructing an Inflationary Potential
  10. The Amount of Inflation and Primordial Fluctuations
  11. Escape from Inflation
  12. The Post-inflationary Phase
  13. Conclusion
  14. Acknowledgements

Figures (2)

  • Figure 1: The graph of $\frac{U(x)}{U_0}$ for $K_1=3, \gamma=3, \lambda =1, \epsilon =10$. There exists a non-supersymmetric AdS minimum.
  • Figure 3: The graph of $\frac{\tilde{U}(x)}{U_0}$ in the regime $x<<1$ for $a_2=2.95, \gamma=1, \frac{C_1}{U_0} =3.01, C_2 =1$. There exists a dS minimum.