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Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation

Jon Brown, William Cottrell, Gary Shiu, Pablo Soler

TL;DR

The paper investigates whether large-field inflation driven by closed-string axions can be embedded in quantum gravity by invoking the Weak Gravity Conjecture. It maps axion/instanton data to particle/gauge data via T-duality and uses the convex-hull criterion to derive quantitative bounds on axion decay constants, showing that in perturbative control all decay constants remain sub-Planckian even with multiple axions. It also analyzes potential loopholes, discrete symmetries, torsion-cycle constructions, and holographic tensions, concluding that many natural inflation scenarios are at odds with WGC constraints and holography. The work highlights a deep connection between quantum gravity consistency conditions and inflationary model-building, suggesting that trans-Planckian field excursions in string theory face robust obstacles and motivating exploration of alternative UV completions or inflationary mechanisms.

Abstract

In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T-duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to discrete symmetries and its possible impact on models with axion monodromy, and the distinction between the strong and mild versions of the WGC. Finally, we offer some speculations regarding the import of these results to the general theory of inflation.

Fencing in the Swampland: Quantum Gravity Constraints on Large Field Inflation

TL;DR

The paper investigates whether large-field inflation driven by closed-string axions can be embedded in quantum gravity by invoking the Weak Gravity Conjecture. It maps axion/instanton data to particle/gauge data via T-duality and uses the convex-hull criterion to derive quantitative bounds on axion decay constants, showing that in perturbative control all decay constants remain sub-Planckian even with multiple axions. It also analyzes potential loopholes, discrete symmetries, torsion-cycle constructions, and holographic tensions, concluding that many natural inflation scenarios are at odds with WGC constraints and holography. The work highlights a deep connection between quantum gravity consistency conditions and inflationary model-building, suggesting that trans-Planckian field excursions in string theory face robust obstacles and motivating exploration of alternative UV completions or inflationary mechanisms.

Abstract

In this note we show that models of natural inflation based on closed string axions are incompatible with the weak gravity conjecture (WGC). Specifically, we use T-duality in order to map the bounds on the charge-to-mass ratio of particles imposed by the WGC, to constraints on the ratio between instanton actions and axion decay constants. We use this connection to prove that if the WGC holds, even when multiple axions are present and mix with each other, one cannot have large axion decay constants while remaining in a regime of perturbative control. We also discuss the extension of the WGC to discrete symmetries and its possible impact on models with axion monodromy, and the distinction between the strong and mild versions of the WGC. Finally, we offer some speculations regarding the import of these results to the general theory of inflation.

Paper Structure

This paper contains 16 sections, 43 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Weak Gravity Conjecture
  3. The conjecture
  4. The Convex Hull Condition
  5. Generaliztion to $p$-form symmetries
  6. Discrete symmetries and the WGC
  7. Mapping instantons and axions to particles and gauge fields
  8. Setup
  9. T-Duality
  10. Black Holes
  11. WGC constraints on axions
  12. General limits on axion inflation
  13. A possible loophole
  14. Torsion Cycles and Generalized WGC
  15. Tension with Holography
  16. ...and 1 more sections

Figures (2)

  • Figure 1: The convex hull condition as applied to two $U(1)$ groups. Vectors corresponding to extremal black holes lie on the unit circle, while non-extremal black holes lie inside the unit disc. On the left (right) hand side, the convex hull defined by the $\vec{z}$ vectors of two (three) charged particles and their antiparticles (blue arrows) ensure the WGC is satisfied.
  • Figure 2: Two situations in which the convex hull condition is not satisfied. Black holes within the unit disk but outside of the convex hull of the two particles (blue areas) are stable and lead to an infinite number of remnants.