Stringy Constraints on Modular Flavor Models

TL;DR

This paper explores string-derived constraints on the moduli space in modular flavor models, revealing certain large-volume and self-dual points are incompatible with string theory, impacting phenomenological model building.

Contribution

It systematically derives stringy constraints on moduli in heterotic orbifold models, highlighting forbidden regions relevant for flavor model predictions.

Findings

Large flavor-modulating modulus values are in the Swampland.

The self-dual point is disfavored in large volume regimes.

Constraints depend on dilaton, beta-function, and modulus ratios.

Abstract

We investigate stringy constraints on moduli spaces in modular flavor models by analyzing moduli-dependent threshold corrections in heterotic string vacua. While moduli play a crucial role in determining the flavor structure of fermions predicted by modular flavor models, the parameter space in which their vacuum expectation values are allowed has not been fully explored. In this work, within the framework of perturbative heterotic string theory on toroidal orbifolds, we derive constraints on the moduli space and study their systematic behavior. We characterize the stringy constraints in terms of the dilaton, the beta-function coefficients, and the ratio between a complex-structure modulus and a K\"ahler modulus. It is found that the large value of the modulus controlling the flavor structure, i.e., $\tau\simeq i \infty$, lies in the Swampland, and the self-dual point $\tau=i$ is also disfavored in the large volume regime of toroidal backgrounds. In addition, we discuss the phenomenological implications of these stringy constraints.