Related papers: Modular Flavor Symmetry on Magnetized Torus
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…
Modular flavor symmetries have been proposed as a new way to address the flavor problem. It is known that they can emerge from string compactifications. We discuss this connection in detail, and show how the congruence subgroups of SL(2,Z),…
We study the flavor structures of zero-modes, which are originated from the modular symmetry on $T^2_1\times T^2_2$ and its orbifold with magnetic fluxes. We introduce the constraint on the moduli parameters by $\tau_2=N\tau_1$, where…
In the modular invariant flavor model of $\rm A_4$, we study the hierarchical structure of lepton/quark flavors at nearby fixed points of $\tau=i$ and $\tau=\omega$ of the modulus, which are in the fundamental domain of $\rm…
The formalism of non-holomorphic modular flavor symmetry is developed, and the Yukawa couplings are level $N$ polyharmonic Maa{\ss} forms satisfying the Laplacian condition. We find that the integer (even) weight polyharmonic Maa{\ss} forms…
In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations of…
We explore a new class of supersymmetric models for lepton masses and mixing angles where the role of flavour symmetry is played by modular invariance. The building blocks are modular forms of level N and matter supermultiplets, both…
We revisit the modular flavor symmetry from a more general perspective. The scalar modular forms of principal congruence subgroups are extended to the vector-valued modular forms, then we have more possible finite modular groups including…
We study the problem of modulus stabilisation in the framework of the modular symmetry approach to the flavour problem. By analysing simple UV-motivated CP-invariant potentials for the modulus $\tau$ we find that a class of these potentials…
We discuss non-invertible symmetries in toroidal compactifications of higher dimensional Yang-Mills theory with magnetic fluxes, which can be regarded as an effective action of type IIB string theory with magnetized D-branes. Specifically,…
We study quark and lepton flavor structures on magnetized $T^2/\mathbb{Z}_2$ twisted orbifold model. There are 6,460 number of flavor models but most of them cannot lead to realistic flavor observables because of the difficulties on…
In the formalism of the non-supersymmetric modular invariance approach to the flavour problem the elements of the Yukawa coupling and fermion mass matrices are expressed in terms of polyharmonic Maa{\ss} modular forms of level $N$ in…
We develop a bottom-up approach to flavour models which combine modular symmetry with orbifold constructions. We first consider a 6d orbifold $\mathbb{T}^2/\mathbb{Z}_N$, with a single torus defined by one complex coordinate $z$ and a…
We discuss the flavor structure in a resolutions of magnetized $T^2/\mathbb{Z}_2$ orbifold models. The flavor structure of Yukawa couplings among chiral zero-modes is sensitive to radii of the resolved fixed points of $T^2/\mathbb{Z}_2$…
We initiate the study of the generalized global flavor symmetries of the Standard Model. The presence of nonzero triangle diagrams between the $U(3)^5$ flavor currents and the $U(1)_Y$ hypercharge current intertwines them in the form of a…
String compactifications on an orbi-folded torus with complex structure give rise to chiral fermions, spontaneously broken CP, modular invariance. We show that this allows simple effective theories of flavour and CP where: i) the QCD angle…
Modular transformations of string theory (including the well-known stringy dualities) play a crucial role in the discussion of discrete flavor symmetries in the Standard Model. They are at the origin of CP transformations and provide a…
We review the modular flavor symmetric models of quarks and leptons focusing on our works. We present some flavor models of quarks and leptons by using finite modular groups and discuss the phenomenological implications. The modular flavor…
As the effective field theory of the superstring theory, ten-dimensional ${\cal N}=1$ supersymmetric Yang-Mills theory is induced. We consider the ten-dimensional space-time ${\cal M}_{10}$ as direct products of our four-dimensional…
Modular flavor symmetry can be used to explain the quark and lepton flavor structures. The SUSY partners of quarks and leptons, which share the same superpotential with the quarks and leptons, will also be constrained by the modular flavor…