Systematics of Aligned Axions

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.

arXiv comment68 pages, 17 figures

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• Recent Progress in the Physics of Axions and Axion-Like Particles
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• Experimental Targets for Photon Couplings of the QCD Axion
• Swampland Conjectures and Late-Time Cosmology
• A Systematic Approach to Kähler Moduli Stabilisation
• Axions of Evil
• Manyfield Inflation in Random Potentials
• Systematics of Aligned Axions
• Pole N-flation
• Axion Landscape Cosmology
• Hessian eigenvalue distribution in a random Gaussian landscape
• Axion Hilltops, Kahler Modulus Quintessence and the Swampland Criteria
• Inflation in Random Landscapes with two energy scales
• Irrational Monodromies of Vacuum Energy
• Instanton Resummation and the Weak Gravity Conjecture