相关论文: Completing the eclectic flavor scheme of the $\bol…

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…

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…

The incorporation of Wilson lines leads to an extension of the modular symmetries of string compactification beyond $\mathrm{SL}(2,\mathbb Z)$. In the simplest case with one Wilson line $Z$, K\"ahler modulus $T$ and complex structure…

We examine a common origin of four-dimensional flavor, CP, and $U(1)_R$ symmetries in the context of heterotic string theory with standard embedding. We find that flavor and $U(1)_R$ symmetries are unified into the $Sp(2h+2, \mathbb{C})$…

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),…

In a consistent top-down approach based on orbifold compactifications, modular and traditional flavor symmetries combine nontrivially to the so-called eclectic flavor symmetry. We extend this scheme from two extra dimensions, discussed…

We discuss aspects of a promising top-down origin of flavor symmetries in particle physics. Modular transformations originating from string theory dualities are shown to play a crucial role. We introduce the notion of an "eclectic" flavor…

A top-down approach to the flavor problem motivated from string theory leads to the concept of eclectic flavor groups that combine traditional and modular flavor symmetries. To make contact with models constructed in the bottom-up approach,…

We show that the recently constructed 5-dimensional supersymmetric $S^1/(Z_2\times Z_2')$ orbifold GUT models allow an appealing explanation of the observed hierarchical structure of the quark and lepton masses and mixing angles. Flavor…

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…

String theory leads to a flavor scheme where modular symmetries play a crucial role. Together with the traditional flavor symmetries they combine to an eclectic flavor group, which we determine via outer automorphisms of the Narain space…

The framework of compactified heterotic string theory offers consistent ultraviolet (UV) completions of the Standard Model (SM) of particle physics. In this approach, the existence of flavor symmetries beyond the SM is imperative and the…

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…

Eclectic flavor groups arising from string compactifications combine the power of modular and traditional flavor symmetries to address the flavor puzzle. This top-down scheme determines the representations and modular weights of all matter…

The framework of compactified heterotic string theory offers consistent ultraviolet (UV) completions of the Standard Model (SM) of particle physics. In this approach, the existence of flavor symmetries beyond the SM is imperative and the…

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…

Effective field theories arising from string compactifications are subject to constraints originating from the duality transformations of string theory. Interpreting these so-called selection rules in terms of conventional symmetries has…

A top-down approach to the flavor puzzle leads to eclectic flavor groups which include modular and traditional flavor symmetries. Based on examples of semirealistic T2/Z3 orbifold compactifications of heterotic string theory, we discuss the…

We study the modular symmetry of localized modes on fixed points of $T^2/\mathbb{Z}_2$ orbifold. First, we find that the localized modes with even (odd) modular weight generally have $\Delta(6n^2)$ ($\Delta'(6n^2)$) modular flavor symmetry.…

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…