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 $e^{2\ddot{I}€i\ddot{I}„}$ and to a light axion identified as $\mathrm{Re}\ddot{I}„$, where $\ddot{I}„$ is the modulus field. This stabilization mechanism provides the axion solution to the strong CP problem. The potential has a minimum at a large $\mathrm{Im}\ddot{I}„$ which suppresses explicit $U(1{)}_{\mathrm{PQ}}$ violation terms proportional to $e^{-2\ddot{I}€\mathrm{Im}\ddot{I}„}$, and hence the quality of the axion is ensured by the residual symmetry associated with the $T$-transformation, $\ddot{I}„\to \ddot{I}„+1$, around the fixed point $\ddot{I}„\sim i\infty$.

10 pages, 2 figures; ver2 matched to published version