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 e2πiτ and to a light axion identified as Reτ, where τ is the modulus field. This stabilization mechanism provides the axion solution to the strong CP problem. The potential has a minimum at a large Imτ which suppresses explicit U(1)PQ violation terms proportional to e−2πImτ, and hence the quality of the axion is ensured by the residual symmetry associated with the T-transformation, τ → τ + 1, around the fixed point τ ∼ i∞.