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Towards Axion Monodromy Inflation with Warped KK-Modes

Arthur Hebecker, Jakob Moritz, Alexander Westphal, Lukas T. Witkowski

TL;DR

The authors propose a minimal axion monodromy model in a Klebanov-Strassler throat where the inflaton is the lightest KK mode of the RR-2-form $C_2$ on a shrinking $S^2$. The monodromy arises from the cycle's homological triviality and a double-throat geometry, yielding an ultra-light mode suppressed by warp factors, with back-reaction becoming important only near Planck-scale excursions. They develop a 5d RS-like effective theory and a prescription to extract the back-reacted 4d potential from static 5d solutions, then outline the full Type IIB equations and boundary conditions needed for a numerical study of the back-reaction. Despite the need for numerical analysis, the setup offers a simple, tractable setting to explore large-field inflation in string theory while avoiding brane-backreaction complications.

Abstract

We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential $C_2$ in the standard Klebanov-Strassler throat. One can think of this inflaton candidate as being defined by the integral of $C_2$ over the $S^2$ cycle of the throat. It obtains an exponentially small mass from the IR-region in which the $S^2$ shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. Crucially, the $S^2$ cycle has to be shared between two throats, such that the second locus where the $S^2$ shrinks is also in a warped region. Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. However, the inflaton back-reaction starts to deform the geometry strongly once the field excursion approaches the Planck scale. We derive the system of differential equations required to treat this effect quantitatively. Numerical work is required to decide whether back-reaction makes the model suitable for realistic inflation. While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong. Also, the mere existence of our ultra-light throat mode (with double exponentially suppressed mass) is noteworthy.

Towards Axion Monodromy Inflation with Warped KK-Modes

TL;DR

The authors propose a minimal axion monodromy model in a Klebanov-Strassler throat where the inflaton is the lightest KK mode of the RR-2-form on a shrinking . The monodromy arises from the cycle's homological triviality and a double-throat geometry, yielding an ultra-light mode suppressed by warp factors, with back-reaction becoming important only near Planck-scale excursions. They develop a 5d RS-like effective theory and a prescription to extract the back-reacted 4d potential from static 5d solutions, then outline the full Type IIB equations and boundary conditions needed for a numerical study of the back-reaction. Despite the need for numerical analysis, the setup offers a simple, tractable setting to explore large-field inflation in string theory while avoiding brane-backreaction complications.

Abstract

We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential in the standard Klebanov-Strassler throat. One can think of this inflaton candidate as being defined by the integral of over the cycle of the throat. It obtains an exponentially small mass from the IR-region in which the shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. Crucially, the cycle has to be shared between two throats, such that the second locus where the shrinks is also in a warped region. Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. However, the inflaton back-reaction starts to deform the geometry strongly once the field excursion approaches the Planck scale. We derive the system of differential equations required to treat this effect quantitatively. Numerical work is required to decide whether back-reaction makes the model suitable for realistic inflation. While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong. Also, the mere existence of our ultra-light throat mode (with double exponentially suppressed mass) is noteworthy.

Paper Structure

This paper contains 14 sections, 91 equations, 3 figures.

Table of Contents

  1. Introduction
  2. The Double Throat
  3. A Simple Geometric Setup and Reduction to 5d
  4. KK-Reduction on the Effective 5d-Throat and the 4d Action
  5. Simple Consistency Checks from Energetics and Mass Scales
  6. Energy Density at the boundary of $S^3_{1/2}$
  7. Inflaton Energy Density vs $F_3$-Flux Energy Density
  8. The Ultra-light Mode in the KS background
  9. A Simple Prescription for Obtaining the Back-reacted Potential
  10. The Type IIB Equations of Motion
  11. The Ansatz and Boundary Conditions
  12. Comparison with the Wilson-Contour of $B_2$
  13. Conclusion
  14. The Equations of Motion

Figures (3)

  • Figure 1: The double throat: The dashed line indicates the family of $S^2$'s bending around into the second throat, shrinking to zero size at the tips.
  • Figure 2: The geometry close to the tip of the throat.
  • Figure 3: The bound state and first excited solutions with $kL=5 \pi$ and $\Lambda=100 \pi/L$ ($r_c/L\approx 0.06$), plotted in the range $0\leq y \leq 0.2 \,L$