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Backreacted Axion Field Ranges in String Theory

Florent Baume, Eran Palti

TL;DR

The paper investigates whether axions in Type IIA string theory can achieve super-Planckian excursions when monodromy or alignment mechanisms are active. By explicitly computing how axion vacuum energy backreacts on the moduli and the axion field-space metric across Calabi-Yau and twisted-torus compactifications, the authors uncover a universal two-regime behavior: a mild backreaction up to a critical axion value, followed by strong backreaction that renders the proper distance to grow at most logarithmically with the vev. Crucially, the final proper distance up to the critical value is flux-independent, and in alignment scenarios flux backreaction cancels any naive enhancement of the effective decay constant, preserving sub-Planckian limits. The results strengthen swampland expectations about constraints on large-field inflation from string theory and illustrate robust backreaction mechanisms that censor super-Planckian axion excursions across multiple geometric frameworks.

Abstract

String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter is unconstrained by tadpoles and can in principle lead to a parametrically enhanced effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement.

Backreacted Axion Field Ranges in String Theory

TL;DR

The paper investigates whether axions in Type IIA string theory can achieve super-Planckian excursions when monodromy or alignment mechanisms are active. By explicitly computing how axion vacuum energy backreacts on the moduli and the axion field-space metric across Calabi-Yau and twisted-torus compactifications, the authors uncover a universal two-regime behavior: a mild backreaction up to a critical axion value, followed by strong backreaction that renders the proper distance to grow at most logarithmically with the vev. Crucially, the final proper distance up to the critical value is flux-independent, and in alignment scenarios flux backreaction cancels any naive enhancement of the effective decay constant, preserving sub-Planckian limits. The results strengthen swampland expectations about constraints on large-field inflation from string theory and illustrate robust backreaction mechanisms that censor super-Planckian axion excursions across multiple geometric frameworks.

Abstract

String theory axions are interesting candidates for fields whose potential might be controllable over super-Planckian field ranges and therefore as possible candidates for inflatons in large field inflation. Axion monodromy scenarios are setups where the axion shift symmetry is broken by some effect such that the axion can traverse a large number of periods potentially leading to super-Planckian excursions. We study such scenarios in type IIA string theory where the axion shift symmetry is broken by background fluxes. In particular we calculate the backreaction of the energy density induced by the axion vacuum expectation value on its own field space metric. We find universal behaviour for all the compactifications studied where up to a certain critical axion value there is only a small backreaction effect. Beyond the critical value the backreaction is strong and implies that the proper field distance as measured by the backreacted metric increases at best logarithmically with the axion vev, thereby placing strong limitations on extending the field distance any further. The critical axion value can be made arbitrarily large by the choice of fluxes. However the backreaction of these fluxes on the axion field space metric ensures a precise cancellation such that the proper field distance up to the critical axion value is flux independent and remains sub-Planckian. We also study an axion alignment scenario for type IIA compactifications on a twisted torus with four fundamental axions mixing to leave an axion with an effective decay constant which is flux dependent. There is a choice of fluxes for which the alignment parameter is unconstrained by tadpoles and can in principle lead to a parametrically enhanced effective decay constant. However we show that these fluxes backreact on the fundamental decay constants so as to precisely cancel any enhancement.

Paper Structure

This paper contains 11 sections, 84 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Axion monodromy and backreaction
  3. Ramond-Ramond axions
  4. Single field models
  5. Calabi-Yau Models
  6. Twisted Torus Models
  7. Neveu-Schwarz axions
  8. Axion alignment and backreaction
  9. Three axion alignment toy model
  10. Axion alignment on a twisted torus
  11. Summary

Figures (3)

  • Figure 1: Plots showing the moduli $\tilde{s}$ and $\tilde{u}$ as a function of $\rho' = \rho - \rho_0$ for displacement of $\rho'$ along branch 2 of (\ref{['branches']}). The plots are for flux value $f=6$ and show the same function over two different ranges so as to show the behaviour up to $\rho_{\mathrm{crit}} \simeq f^{\frac{3}{2}} \simeq 15$, and the asymptotic behaviour of $\tilde{u}$.
  • Figure 2: Plot showing $\tilde{s}$ as a function of $\rho'$ for the case of a twisted torus compactification with fluxes $\tilde{e}_1=-6$ and $\tilde{l}=1$.
  • Figure 3: Plots showing the moduli $\tilde{t}$ as a function of $v' = v- v_0$ for displacement of $v'$ along both branches (\ref{['branches']}). They are given for flux value $f=6$. The range is chosen such that it is possible to see the asymptotic linear behaviour is reached after $v'$ reaches its critical value \ref{['NScritVal']}.