Metaplectic flavor symmetries from magnetized tori

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.

Modular symmetry and zeros in magnetic compactifications

“…the new mode functions ξ j S therefore satisfy the original boundary conditions (2.7) again. This is the result for α 1 = α 2 = 0 in the literature [49,51,60]. Note that by construction, the same holds for any α 1 and α 2 .…”

“…the boundary conditions (2.7) remain valid for the T -transformed wave functions ξ j T , and thus the result in [60] is verified. As seen later, a variety of evidence related to zeros of ξ j T and the mode counting formula on the orbifolds supports this choice.…”

“…In a series of papers [49,51,60], there has appeared a puzzle concerning boundary conditions: whether the wave functions satisfy the common (pseudo-)periodicity conditions before and after the modular transformation or not. In this paper, we clarify the puzzle, concentrating on the zeros of the wave functions in the magnetic compactifications.…”

Completing the eclectic flavor scheme of the ℤ2 orbifold

“…In more detail, the traditional flavor symmetry of ref. [1] is extended from [32,49] This picture reveals the fact that the top-down discussion of modular flavor symmetry constitutes an extremely restrictive scenario, which is confirmed in other top-down scenarios [38][39][40][41][42]. As in the case of the bottom-up discussion, firstly the role of (otherwise freely chosen) flavons is played by the moduli T and U , and secondly we arrive at a specific finite modular group, being…”

Modular origin of mass hierarchy: Froggatt-Nielsen like mechanism

“…The modular symmetry is originally inspired by string compactifications [53][54][55][56][57][58][59]. From the stringy perspective, the coupling constants and dynamical fields transform under the homogeneous modular group rather than the inhomogeneous modular group [39,40,[60][61][62][63][64] and metaplectic group [65]. Hence we consider modular symmetric model based on Γ in this paper.…”