Axion decay constants away from the lamppost

TL;DR

This work investigates whether quantum gravity constrains axion field ranges by exploiting extended supersymmetry to access strongly coupled regions of Calabi–Yau moduli spaces. Using mirror symmetry, it computes the Kähler metric eigenvalues for one- and two-modulus Calabi–Yau compactifications, showing that duality-induced fundamental regions cap the axion decay constants near the Planck scale, with the largest examples yielding up to a few times $M_P$. Specifically, maximal ranges of about $3.25\,M_P$ for one-parameter and $1.4\,M_P$ for two-parameter models emerge, while instanton corrections are generally subleading. The results emphasize that geometric data (intersection numbers, Euler characteristics) and moduli-space singularities govern the bound, offering insights for inflationary model-building based on axions and suggesting directions for extending the analysis to broader Calabi–Yau families and F-theory open-string moduli.

Abstract

It is unknown whether a bound on axion field ranges exists within quantum gravity. We study axion field ranges using extended supersymmetry, in particular allowing an analysis within strongly coupled regions of moduli space. We apply this strategy to Calabi-Yau compactifications with one and two Kähler moduli. We relate the maximally allowable decay constant to geometric properties of the underlying Calabi-Yau geometry. In all examples we find a maximal field range close to the reduced Planck mass (with the largest field range being 3.25 $M_P$). On this perspective, field ranges relate to the intersection and instanton numbers of the underlying Calabi-Yau geometry.

Figures (7)

• Figure 1: Fundamental domain under the discrete $SL(2, \mathbb{Z})$ of the dilaton-axion system.
• Figure 2: Plot of the axion field range for the one-parameter quintic threefold without $\alpha'$-corrections (grey), for the full tree-level Kähler potential (blue), and including instanton contributions up to order ten (dotted orange).
• Figure 3: Fundamental domain of the Kähler modulus of the quintic.
• Figure 4: Eigenvalues of the Kähler metric for $\mathbb{P}^4_{(1,1,1,6,9)}[18]$ derived from the prepotential in \ref{['eq:p11169prepotential']} with no instanton contributions.
• Figure 5: Contour lines of $|\psi|={\rm const.}$ for $T_{1}$ (left) and $T_{2}$ (right). $T_2$ is fixed and $T_1$ varies by varying $\psi.$ For small $\psi$ (not shown here) the behaviour becomes non-trivial. There are in principle three distinct solutions to $\phi^3=1$, however the contours remain the same for sufficiently large values for $|\psi|.$