Notes on natural inflation

TL;DR

The paper addresses how natural inflation can be realized without requiring a super-Planckian decay constant by leveraging nonperturbative dynamics of strongly coupled gauge theories. Through large-N dynamics and a softly broken ${ m N}=1$ SYM framework, it shows that the axion inflaton can experience a monodromic, multivalued potential, effectively enhancing the decay constant to $f_{ m eff}=N f$. The resulting inflaton potential takes a cosine form with an enlarged period, enabling chaotic inflation with sub-Planckian microscopic decay constants for moderate $N$ or dual Coxeter numbers $h$ of other gauge groups. The work also discusses metastable vacua longevity, possible UV embeddings in supergravity/string theory, and implications for high-scale SUSY breaking scenarios. Overall, it provides a controlled, gauge-theory-based realization of axion monodromy natural inflation with clear paths toward UV completion.

Abstract

In the so-called natural inflation, an axion-like inflaton is assumed to have a cosine-type periodic potential. This is not the case in a very simple model in which the axion-like inflaton is coupled to an SU(N) (or other) pure Yang-Mills, at least in the large N limit as pointed out by Witten. It has a multi-valued potential, which is effectively quadratic, i.e., there is only a mass term in the large N limit. Thanks to this property, chaotic inflation can be realized more naturally with the decay constant of the axion-like inflaton less than the Planck scale. We demonstrate these points explicitly by using softly broken ${\mathcal N}=1$ Super-Yang-Mills which allows us to treat finite N. This analysis also suggests that moderately large gauge groups such as $E_{8}$ are good enough with a Planck scale decay constant.