Symplectic modular symmetry in heterotic string vacua: flavor, CP, and R-symmetries

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, ℂ) modular symmetries of Calabi-Yau threefolds with h being the number of moduli fields. Together with the $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP CP symmetry, they are enhanced to GSp(2h + 2, ℂ) ≃ Sp(2h + 2, ℂ) ⋊ $$ {\mathbb{Z}}_2^{\mathrm{CP}} $$ ℤ 2 CP generalized symplectic modular symmetry. We exemplify the S3, S4, T′, S9 non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and ℤ2, S4 flavor symmetries on three-parameter examples of Calabi-Yau threefolds. Thus, non-trivial flavor symmetries appear in not only the exact orbifold limit but also a certain class of Calabi-Yau three-folds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

Flavor symmetries in an SU(5) model of grand unification

We investigate the options for imposing flavor symmetries on a minimal renormalizable non-supersymmetric SU(5) grand unified theory, without introducing additional flavor-related fields. Such symmetries reduce the number of free parameters in the model and therefore lead to more predictive models. We consider the Yukawa sector of the Lagrangian, and search for all possible flavor symmetries. As a result, we find 25 distinct realistic flavor symmetry cases, with ℤ2, ℤ3, ℤ4, and U(1) symmetries, and no non-Abelian cases.

Entanglement minimization in hadronic scattering with pions

Recent work [S. R. Beane, D. B. Kaplan, N. Klco and M. J. Savage, Phys. Rev. Lett. 122, 102001 (2019), arXiv:1812.03138.] conjectured that entanglement is minimized in low-energy hadronic scattering processes. It was shown that the minimization of the entanglement power (EP) of the low-energy baryon–baryon [Formula: see text]-matrix implies novel spin–flavor symmetries that are distinct from large-[Formula: see text] QCD predictions and are confirmed by high-precision lattice QCD simulations. Here, the conjecture of minimal entanglement is investigated for scattering processes involving pions and nucleons. The EP of the [Formula: see text]-matrix is constructed for the [Formula: see text] and [Formula: see text] systems, and the consequences of minimization of entanglement are discussed and compared with large-[Formula: see text] QCD expectations.

Flavor symmetries in the Yukawa sector of non-supersymmetric SO(10): numerical fits using renormalization group running

We consider a class of SO(10) models with flavor symmetries in the Yukawa sector and investigate their viability by performing numerical fits to the fermion masses and mixing parameters. The fitting procedure involves a top-down approach in which we solve the renormalization group equations from the scale of grand unification down to the electroweak scale. This allows the intermediate scale right-handed neutrinos and scalar triplet, involved in the type I and II seesaw mechanisms, to be integrated out at their corresponding mass scales, leading to a correct renormalization group running. The result is that, of the 14 models considered, only two are able to fit the known data well. Both these two models correspond to ℤ2 symmetries. In addition to being able to fit the fermion masses and mixing parameters, they provide predictions for the sum of light neutrino masses and the effective neutrinoless double beta decay mass parameter, which are both within current observational bounds.

Flavour observables and composite dynamics: leptons

We review lepton flavor physics and corresponding observables in the composite Higgs framework with partial compositeness, considering ‘UV complete’ setups as well as effective and holographic approaches. This includes anarchic flavor setups, scenarios with flavor symmetries, and minimal incarnations of the see-saw mechanism that naturally predict non-negligible lepton compositeness. We focus on lepton flavor violating processes, dipole moments, and on probes of lepton flavor universality, all providing stringent tests of partial compositeness. We discuss the expected size of effects in the different approaches to lepton flavor, which will be useful to understand how a composite lepton sector could look like, given up-to-date experimental constraints.

Completing the eclectic flavor scheme of the ℤ2 orbifold

We present a detailed analysis of the eclectic flavor structure of the two-dimensional ℤ2 orbifold with its two unconstrained moduli T and U as well as SL(2, ℤ)T× SL(2, ℤ)U modular symmetry. This provides a thorough understanding of mirror symmetry as well as the R-symmetries that appear as a consequence of the automorphy factors of modular transformations. It leads to a complete picture of local flavor unification in the (T, U) modulus landscape. In view of applications towards the flavor structure of particle physics models, we are led to top-down constructions with high predictive power. The first reason is the very limited availability of flavor representations of twisted matter fields as well as their (fixed) modular weights. This is followed by severe restrictions from traditional and (finite) modular flavor symmetries, mirror symmetry, $$ \mathcal{CP} $$ CP and R-symmetries on the superpotential and Kähler potential of the theory.

Metaplectic flavor symmetries from magnetized tori

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.

Flavor symmetries of six-dimensional $$ \mathcal{N} $$ = (1, 0) theories from AdS/CFT correspondence

We calculate the superconformal indices of a class of six-dimensional $$ \mathcal{N} $$ N = (1, 0) superconformal field theories realized on M5-branes at ℂ2/ℤk singularity by using the method developed in previous works of the authors and collaborators. We use the AdS/CFT correspondence, and finite N corrections are included as the contribution of M2-branes wrapped on two-cycles in S4/ℤk. We confirm that the indices are consistent with the expected flavor symmetries.