Radiative correction on moduli stabilization in modular flavor symmetric models

We study the radiative corrections to the stabilization of the complex structure modulus in modular flavor symmetric models. We discuss the possibility of obtaining the vacuum expectation value of in the vicinity of the fixed point where residual symmetries remain unbroken. As concrete examples, we analyze the one-loop Coleman-Weinberg potential in the A₄ modular flavor models. We show that the one-loop correction may lead to the slight deviation from the tree-level result, which may realize a phenomenologically preferred value of the complex structure modulus, particularly when the number of species contributing to the one-loop correction is large enough.