Related papers: Flavored modular differential equations

We present a flavor model with the $S_3$ modular invariance in the framework of SU(5) GUT. The $S_3$ modular forms of weights $2$ and $4$ give the quark and lepton mass matrices with a common complex parameter, the modulus $\tau$. The GUT…

The relaxed highest weight representations introduced by Feigin et al. are a class of representations of the affine Kac-Moody algebra $\hat{\mathfrak{sl}_2}$, which do not have a highest (or lowest) weight. We formulate a generalization of…

We study a flavor model with $A_4$ symmetry which originates from $S_4$ modular group. In $S_4$ symmetry, $Z_2$ subgroup can be anomalous, and then $S_4$ can be violated to $A_4$. Starting with a $S_4$ symmetric Lagrangian at the tree…

We propose an interesting assignment of positive modular wights for fields in a modular non-Abelian discrete flavor symmetry. By this assignment, we can construct inverse seesaw and linear seesaw models without any additional symmetries…

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,…

For an untwisted affine Kac-Moody Lie algebra $\mathfrak{g}$ with Cartan and Borel subalgebras $\mathfrak{h} \subset \mathfrak{b} \subset \mathfrak{g}$, affine Demazure modules are certain $U(\mathfrak{b})$-submodules of the irreducible…

We quantitatively analyze a quark-lepton flavour model derived from a six-dimensional supersymmetric theory with $SO(10)\times U(1)$ gauge symmetry, compactified on an orbifold with magnetic flux. Two bulk $\mathbf{16}$-plets charged under…

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…

In this paper, we are interested in the decomposition of the tensor product of two representations of a symmetrizable Kac-Moody Lie algebra $\mathfrak g$. Let $P\_+$ be the set of dominant integral weights. For $\lambda\in P\_+$ ,…

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…

In this paper, we propose a mechanism which induces nontrivial flavor structure from transformations of a noncompact Lie group SL(3,C) in noncommutative geometry. Matrices $L \in$ SL(3,C) are associated with accompanied by the preon fields…

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…

For a dominant integral weight $lambda $, we introduce a family of $U_q ^+ (mathfrak{g})$-submodules $V_w (lambda)$ of the irreducible highest weight $U_q (mathfrak{g})$-module $V(lambda)$ of highest weight $lambda $ for a generalized…

We apply results from the geometry of nilpotent orbits and nilpotent Slodowy slices, together with modularity and asymptotic analysis of characters, to prove many new isomorphisms between affine W-algebras and affine Kac-Moody vertex…

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 study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion…

We present a class of supersymmetric models which address the flavor puzzle and have an inverted hierarchy of sfermions. Their construction involves quiver-like models with link fields in generic representations. The magnitude of…

The mass matrix forms of quarks and leptons are discussed in theory with permutation flavor symmetry. The structure of scalar potential is analyzed in case that electroweak doublet Higgs fields have non-trivial flavor symmetry charges. We…

A four-dimensional effective model with $G_{\rm SM}\times SL(2,\mathbb{Z}) \times U(1)_X$ is proposed in string-derived supergravity framework, where $G_{\rm SM}$ is the Standard Model (SM) gauge group and $U(1)_X$ is gauged. We show…

We study a non-universal flavor scenario at the level of the Standard Model Effective Field Theory, according to which the matrix of Wilson coefficients $c_{uW}$ of an up-type electroweak quark dipole operator is aligned with the up-type…