On the Possibility of Large Axion Decay Constants

TL;DR

This work investigates whether string/M-theory can yield axion-like fields with decay constants $f_A$ larger than the Planck scale $M_p$, a prospect relevant for natural inflation and anthropic explanations of the cosmological constant. Across string theories with varying amounts of supersymmetry, the authors systematically examine moduli from $p$-form fields and Wilson lines, showing that dualities and the appearance of light states or instantons generate substantial higher-harmonic contributions that rescale the effective action to be dominated by harmonics with $n sim f_A/M_p$, thereby preventing slow-roll inflation. In multiple concrete settings, including heterotic, Type I/II, M-theory, and M-theory on $G_2$ manifolds, the would-be large $f_A$ regions map to regimes where the decay constant is bounded by $M_p$ or where the axion potential varies on Planckian scales. The findings suggest a no-go tendency for large axion decay constants within controlled string/M-theory frameworks, though a formal proof remains elusive and the search for potential counterexamples continues.

Abstract

The decay constant of the QCD axion is required by observation to be small compared to the Planck scale. In theories of "natural inflation," and certain proposed anthropic solutions of the cosmological constant problem, it would be interesting to obtain a large decay constant for axion-like fields from microscopic physics. String theory is the only context in which one can sensibly address this question. Here we survey a number of periodic fields in string theory in a variety of string vacua. In some examples, the decay constant can be parameterically larger than the Planck scale but the effective action then contains appreciable harmonics of order $f_A/M_p$. As a result, these fields are no better inflaton candidates than Planck scale axions.