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A<sc>bstract</sc> Discrete flavor symmetries have been an appealing approach for explaining the observed flavor structure, which is not justified in the Standard Model (SM). Typically, these models require a so-called flavon field in order to give rise to the flavor structure upon the breaking of the flavor symmetry by the vacuum expectation value (VEV) of the flavon. Generally, in order to obtain the desired vacuum alignment, a flavon potential that includes additional so-called driving fields is required. On the other hand, allowing the flavor symmetry to be modular leads to a structure where the couplings are all holomorphic functions that depend only on a complex modulus, thus greatly reducing the number of parameters in the model. We show that these elements can be combined to simultaneously explain the flavor structure and dark matter (DM) relic abundance. We present a modular model with flavon vacuum alignment that allows for realistic flavor predictions while providing a successful fermionic DM candidate. 

A<sc>bstract</sc> Inspired by the structure of top-down derived models endowed with modular flavor symmetries, we investigate the yet phenomenologically unexplored binary dihedral group 2D₃. After building the vector-valued modular forms in the representations of 2D₃with small modular weights, we systematically classify all (Dirac and Majorana) mass textures of fermions with fractional modular weights and all possible 2 + 1-family structures. This allows us to explore the parameter space of fermion models based on 2D₃, aiming at a description of both quarks and leptons with a minimal number of parameters and best compatibility with observed data. We consider the separate possibilities of neutrino masses generated by either a type-I seesaw mechanism or the Weinberg operator. We identify a model that, besides fitting all known flavor observables, delivers predictions for six not-yet measured parameters and favors normal-ordered neutrino masses generated by the Weinberg operator. It would be interesting to figure out whether it is possible to embed our model within a top-down scheme, such as$${\mathbb{T}}^{2}/{\mathbb{Z}}_{4}$$heterotic orbifold compactifications. 

A bstract Nontrivial strong dynamics often leads to the appearance of chiral composites. In phenomenological applications, these can either play the role of Standard Model particles or lift chiral exotics by partnering with them in mass terms. As a consequence, the RG flow may change the effective number of chiral generations, a phenomenon we call generation flow. We provide explicit constructions of globally consistent string models exhibiting generation flow. Since such constructions were misclassified in the traditional model searches, our results imply that more care than usually appreciated has to be taken when scanning string compactifications for realistic models. 

A bstract 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.