Finite modular axion and radiative moduli stabilization

Abstract

We propose a simple setup which can stabilize a modulus field of the finite modular symmetry by the Coleman-Weinberg potential. Our scenario leads to a large hierarchy suppressing instanton-like corrections $e^{2\pi i\tau }$ and to a light axion identified as $\mathrm{Re}\tau$, where $\tau$ is the modulus field. This stabilization mechanism provides the axion solution to the strong CP problem. The potential has a minimum at a large $\mathrm{Im}\tau$ which suppresses explicit $U(1{)}_{\mathrm{PQ}}$ violation terms proportional to $e^{-2\pi \mathrm{Im}\tau }$, and hence the quality of the axion is ensured by the residual symmetry associated with the $T$-transformation, $\tau \to \tau +1$, around the fixed point $\tau \sim i\infty$.

Comments: 10 pages, 2 figures; ver2 matched to published version