Metaplectic Flavor Symmetries from Magnetized Tori

TL;DR

This paper explores how magnetic flux compactifications on tori lead to finite metaplectic flavor symmetries, providing analytic Yukawa couplings and insights into flavor structure and model predictivity.

Contribution

It derives closed-form Yukawa couplings for arbitrary fluxes and shows how modular symmetries emerge from the underlying torus geometry, enhancing model control and predictivity.

Findings

Derived analytic expressions for Yukawa couplings with arbitrary fluxes

Identified finite metaplectic groups from modular transformations

Linked flavor suppression to localization in compact space

Abstract

We revisit the flavor symmetries arising from compactifications on tori with magnetic background fluxes. Using Euler's Theorem, we derive closed form analytic expressions for the Yukawa couplings that are valid for arbitrary flux parameters. We discuss the modular transformations for even and odd units of magnetic flux, M, and show that they give rise to finite metaplectic groups the order of which is determined by the least common multiple of the number of zero-mode flavors involved. Unlike in models in which modular flavor symmetries are postulated, in this approach they derive from an underlying torus. This allows us to retain control over parameters, such as those governing the kinetic terms, that are free in the bottom-up approach, thus leading to an increased predictivity. In addition, the geometric picture allows us to understand the relative suppression of Yukawa couplings from their localization properties in the compact space. We also comment on the role supersymmetry plays in these constructions, and outline a path towards non-supersymmetric models with modular flavor symmetries.