Related papers: Flavor symmetries from modular subgroups in magnet…
We study the modular symmetry of zero-modes on $T_1^2 \times T_2^2$ and orbifold compactifications with magnetic fluxes, $M_1,M_2$, where modulus parameters are identified. This identification breaks the modular symmetry of $T^2_1 \times…
We study the moduli stabilization from the viewpoint of modular flavor symmetries. We systematically analyze stabilized moduli values in possible configurations of flux compactifications, investigating probabilities of moduli values and…
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 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…
We study the modular invariance in magnetized torus models. Modular invariant flavor model is a recently proposed hypothesis for solving the flavor puzzle, where the flavor symmetry originates from modular invariance. In this framework…
We study the modular symmetry in $T^2$ and orbifold comfactifications with magnetic fluxes. There are $|M|$ zero-modes on $T^2$ with the magnetic flux $M$. Their wavefunctions as well as massive modes behave as modular forms of weight $1/2$…
We study flavor phenomenologies in a basis of a double covering of modular $A_4$ group with a hidden $SU(2)$ symmetry, in which we work on regions at nearby two fixed points and three special points. These special points of…
We present a detailed analysis of the eclectic flavor structure of the two-dimensional $\mathbb Z_2$ orbifold with its two unconstrained moduli $T$ and $U$ as well as $\mathrm{SL}(2,\mathbb Z)_T\times \mathrm{SL}(2,\mathbb Z)_U$ modular…
We study the modular symmetry in magnetized D-brane models on $T^2$. Non-Abelian flavor symmetry $D_4$ in the model with magnetic flux $M=2$ (in a certain unit) is a subgroup of the modular symmetry. We also study the modular symmetry in…
We study the modular symmetry in magnetized $T^{2g}$ torus and orbifold models. The $T^{2g}$ torus has the modular symmetry $\Gamma_{g}=Sp(2g,\mathbb{Z})$. Magnetic flux background breaks the modular symmetry to a certain normalizer…
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…
Flavor symmetry plays a crucial role in the standard model of particle physics but its origin is still unknown. We develop a new method (based on outer automorphisms of the Narain space group) to determine flavor symmetries within…
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…
Only four $\mathbb{T}^2/\mathbb{Z}_K$ orbifold building blocks are admissible in heterotic string compactifications. We investigate the flavor properties of all of these building blocks. In each case, we identify the traditional and modular…
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…
We study the modular symmetry on magnetized toroidal orbifolds with Scherk-Schwarz phases. In particular, we investigate finite modular flavor groups for three-generation modes on magnetized orbifolds. The three-generation modes can be the…
Modular symmetries naturally combine with traditional flavor symmetries and $\mathcal{CP}$, giving rise to the so-called eclectic flavor symmetry. We apply this scheme to the two-dimensional $\mathbb{Z}_2$ orbifold, which is equipped with…
A multiplicity of quark-lepton families can naturally arise as zero-modes in flux compactifications. The flavour structure of quark and lepton mass matrices is then determined by the wave function profiles of the zero-modes. We consider a…
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…
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 $T^2/\mathbb{Z}_2$…