A note on the predictions of models with modular flavor symmetries

TL;DR

This paper highlights that the predictive power of models with modular flavor symmetries is limited by non-holomorphic corrections in the Kähler potential, which introduce additional parameters and reduce predictivity.

Contribution

It demonstrates that non-holomorphic terms in the Kähler potential affect the predictions of modular flavor symmetry models and discusses ways to potentially preserve their predictivity.

Findings

Non-holomorphic terms introduce corrections to model predictions.

The general Kähler potential contains extra parameters.

Predictive power is reduced due to these additional terms.

Abstract

Models with modular flavor symmetries have been thought to be highly predictive. We point out that these predictions are subject to corrections from non-holomorphic terms in the Lagrangean. Specifically, in the models discussed in the literature, the K\"ahler potential is not fixed by the symmetries, for instance. The most general K\"ahler potential consistent with the symmetries of the model contains additional terms with additional parameters, which reduce the predictive power of these constructions. We also comment on how one may conceivably retain the predictivity.