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 Kähler potential is not fixed by the symmetries, for instance. The most general Kähler 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 potential ways of how one may conceivably retain the predictivity.
Highlights
A rather exciting observation has been made [1, 2]: nine neutrino parameters can be predicted from only three input parameters
The Kahler potential, which contains the information about the fields, is not at all fixed by the symmetries and transformation properties of the models
There exist many additional parameters, and, as a consequence, the number of free parameters is generically larger than the number of predictions
Summary
A rather exciting observation has been made [1, 2]: nine neutrino parameters can be predicted from only three input parameters. The point of this paper is to show that these models have additional parameters which have not been taken into account in the models in the recent literature. To understand the main point of our paper, recall that the predictions of these models come from the fact that the superpotential is fixed by the modular transformations. The Kahler potential, which contains the information about the fields, is not at all fixed by the symmetries and transformation properties of the models. This is why the modular transformations alone do not allow one to make such remarkable predictions, as we shall discuss in more detail in what follows
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