Systematics of Aligned Axions

TL;DR

This paper introduces a new method to analyze complex multi-axion potentials by exploiting approximate symmetries, enabling efficient identification of minima and flat regions relevant for inflation, and extends previous alignment concepts.

Contribution

The authors develop a novel technique leveraging approximate symmetries to analyze large N axion potentials efficiently, improving understanding of their structure and inflationary properties.

Findings

Potential flat regions are enhanced by N^{3/2} in broad classes of theories.

The method accurately locates minima in complex energy landscapes.

The framework unifies and extends previous axion alignment concepts.

Abstract

We describe a novel technique that renders theories of $N$ axions tractable, and more generally can be used to efficiently analyze a large class of periodic potentials of arbitrary dimension. Such potentials are complex energy landscapes with a number of local minima that scales as $\sqrt{N!}$, and so for large $N$ appear to be analytically and numerically intractable. Our method is based on uncovering a set of approximate symmetries that exist in addition to the $N$ periods. These approximate symmetries, which are exponentially close to exact, allow us to locate the minima very efficiently and accurately and to analyze other characteristics of the potential. We apply our framework to evaluate the diameters of flat regions suitable for slow-roll inflation, which unifies, corrects and extends several forms of "axion alignment" previously observed in the literature. We find that in a broad class of random theories, the potential is smooth over diameters enhanced by $N^{3/2}$ compared to the typical scale of the potential. A Mathematica implementation of our framework is available online.