Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry

Understand

We discuss a scheme to implement the relaxion solution to the hierarchy problem with multiple axions, and present a UV-completed model realizing the scheme.

• All of the $N$ axions in our model are periodic with a similar decay constant $f$ well below the Planck scale.
• In the limit $N\gg 1$, the relaxion $\phi$ corresponds to an exponentially long multi-helical flat direction which is shaped by a series of mass mixing between nearby axions in the compact field space of $N$ axions.
• With the length of flat direction given by $\Delta \phi =2\pi f_{\rm eff} \sim e^{\xi N} f$ for $\xi={\cal O}(1)$, both the scalar potential driving the evolution of $\phi$ during the inflationary epoch and the $\phi$-dependent Higgs boson mass vary with an exponentially large periodicity of ${\cal O}(f_{\rm eff})$, while the back reaction potential stabilizing the relaxion has a periodicity of ${\cal O}( f)$.