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On Natural Inflation and Moduli Stabilisation in String Theory

Eran Palti

TL;DR

The paper investigates whether string-theoretic axion alignment can yield super-Planckian decay constants needed for natural inflation. By constructing Type IIA Calabi–Yau flux vacua and analyzing both perturbative moduli stabilization and non-perturbative axion lifting, the authors show that moduli backreaction generically cancels any enhancement from alignment, keeping the light-axion decay constant sub-Planckian. They extend the analysis to general F-term fixing with two and three moduli and to non-supersymmetric vacua, finding the enhancement is not robust across these setups. The results provide quantitative support for a strong version of the Weak Gravity Conjecture in string theory and suggest substantial constraints on large-field inflation scenarios arising from axion alignment, while leaving room for potential exceptions in more exotic compactifications or superpotential structures. Overall, the work clarifies how moduli stabilization interacts with axion alignment and the extent to which string theory permits super-Planckian inflaton excursions.

Abstract

Natural inflation relies on the existence of an axion decay constant which is super-Planckian. In string theory only sub-Planckian axion decay constants have been found in any controlled regime. However in field theory it is possible to generate an enhanced super-Planckian decay constant by an appropriate aligned mixing between axions with individual sub-Planckian decay constants. We study the possibility of such a mechanism in string theory. In particular we construct a new realisation of an alignment scenario in type IIA string theory compactifications on a Calabi-Yau where the alignment is induced through fluxes. Within field theory the original decay constants are taken to be independent of the parameters which induce the alignment. In string theory however they are moduli dependent quantities and so interact gravitationally with the physics responsible for the mixing. We show that this gravitational effect of the fluxes on the moduli can precisely cancel any enhancement of the effective decay constant. This censorship of an effective super-Planckian decay constant depends on detailed properties of Calabi-Yau moduli spaces and occurs for all the examples and classes that we study. We expand these results to a general superpotential assuming only that the axion superpartners are fixed supersymmetrically and are able to show for a large class of Calabi-Yau manifolds, but not all, that the cancellation effect occurs and is independent of the superpotential. We also study simple models where the moduli are fixed non-supersymmetrically and find that similar cancellation behaviour can emerge. Finally we make some comments on a possible generalisation to axion monodromy inflation models.

On Natural Inflation and Moduli Stabilisation in String Theory

TL;DR

The paper investigates whether string-theoretic axion alignment can yield super-Planckian decay constants needed for natural inflation. By constructing Type IIA Calabi–Yau flux vacua and analyzing both perturbative moduli stabilization and non-perturbative axion lifting, the authors show that moduli backreaction generically cancels any enhancement from alignment, keeping the light-axion decay constant sub-Planckian. They extend the analysis to general F-term fixing with two and three moduli and to non-supersymmetric vacua, finding the enhancement is not robust across these setups. The results provide quantitative support for a strong version of the Weak Gravity Conjecture in string theory and suggest substantial constraints on large-field inflation scenarios arising from axion alignment, while leaving room for potential exceptions in more exotic compactifications or superpotential structures. Overall, the work clarifies how moduli stabilization interacts with axion alignment and the extent to which string theory permits super-Planckian inflaton excursions.

Abstract

Natural inflation relies on the existence of an axion decay constant which is super-Planckian. In string theory only sub-Planckian axion decay constants have been found in any controlled regime. However in field theory it is possible to generate an enhanced super-Planckian decay constant by an appropriate aligned mixing between axions with individual sub-Planckian decay constants. We study the possibility of such a mechanism in string theory. In particular we construct a new realisation of an alignment scenario in type IIA string theory compactifications on a Calabi-Yau where the alignment is induced through fluxes. Within field theory the original decay constants are taken to be independent of the parameters which induce the alignment. In string theory however they are moduli dependent quantities and so interact gravitationally with the physics responsible for the mixing. We show that this gravitational effect of the fluxes on the moduli can precisely cancel any enhancement of the effective decay constant. This censorship of an effective super-Planckian decay constant depends on detailed properties of Calabi-Yau moduli spaces and occurs for all the examples and classes that we study. We expand these results to a general superpotential assuming only that the axion superpartners are fixed supersymmetrically and are able to show for a large class of Calabi-Yau manifolds, but not all, that the cancellation effect occurs and is independent of the superpotential. We also study simple models where the moduli are fixed non-supersymmetrically and find that similar cancellation behaviour can emerge. Finally we make some comments on a possible generalisation to axion monodromy inflation models.

Paper Structure

This paper contains 10 sections, 66 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Type IIA moduli stabilisation on a Calabi-Yau with flux
  3. Non-perturbative effects and application to inflation
  4. Flux stabilisation of decay constants
  5. General analysis of F-term fixing of moduli
  6. Two moduli mixing
  7. Three moduli mixing
  8. Non-supersymmetric vacua
  9. Summary
  10. A toy axion monodromy model

Figures (1)

  • Figure 1: Plots showing the effective axion decay constants for the two instantons associated to $u_1$ and $u_2$ as a function of the moduli. The $f_2$ plot is set at $u_2=1$ and the $f_1$ plot at $u_3=1$.