Transplanckian axions !?

TL;DR

This work investigates the viability of transplanckian axion decay constants in the presence of quantum gravity by constructing and evaluating gravitational instantons coupled to axions. It shows that single-axion and lattice-aligned multi-axion schemes are typically spoiled by higher-harmonic instanton contributions, limiting the inflaton field range. A moderate, √N-type enhancement can be realized with N axions only if a discrete Z_N symmetry forbids certain instantons, prompting a generalized WGC that incorporates discrete gauge structure. The authors further connect these semiclassical results to string theory, arguing that D-brane (stringy) instantons reproduce the same qualitative constraints and emphasize careful UV completions in large-field inflation models.

Abstract

We discuss quantum gravitational effects in Einstein theory coupled to periodic axion scalars to analyze the viability of several proposals to achieve superplanckian axion periods (aka decay constants) and their possible application to large field inflation models. The effects we study correspond to the nucleation of euclidean gravitational instantons charged under the axion, and our results are essentially compatible with (but independent of) the Weak Gravity Conjecture, as follows: Single axion theories with superplanckian periods contain gravitational instantons inducing sizable higher harmonics in the axion potential, which spoil superplanckian inflaton field range. A similar result holds for multi-axion models with lattice alignment (like the Kim-Nilles-Peloso model). Finally, theories with $N$ axions can still achieve a moderately superplanckian periodicity (by a $\sqrt{N}$ factor) with no higher harmonics in the axion potential. The Weak Gravity Conjecture fails to hold in this case due to the absence of some instantons, which are forbidden by a discrete $\mathbf{Z}_N$ gauge symmetry. Finally we discuss the realization of these instantons as euclidean D-branes in string compactifications.

Figures (6)

• Figure 1: Different choices of basis for N-flation (left) and kinetic alignment (right) models.
• Figure 2: Different choices of basis in KNP models. The red line always correspond to the inflationary trajectory.
• Figure 3: Instanton action for a model of N-flation with two axions (left) and a model of kinetic alignment (right). The red line corresponds to the direction of the inflationary trajectory.
• Figure 4: Gravitational effects for a model of lattice alignment. The blue ellipse represents the region for which the instanton action is small and its effect over the axion can not be neglected. The red line corresponds to the direction of the inflationary trajectory.
• Figure 5: Pictorial representation of the euclidean string (thick black line) and its associated Dirac domain wall (blue shaded circle). When we move an instanton around the dashed circle, it picks an extra phase as it crosses the domain wall. This phase must be trivial for the theory to be consistent.