Modular Zeros

ArXiv.org · 2025-12-24

Modular symmetries are known to be powerful and have various remarkable properties. We point out that the structure of vector-valued modular forms (VVMFs) space leads to the absence of couplings which cannot be explained in terms of the usual symmetries. These modular zeros, which correspond to gaps in spaces of VVMFs, have the power of explaining certain stringy zeros, and to explain the renowned Weinberg texture that relates the Cabibbo angle to the hierarchies of the light down and strange quarks.

Multiple realizations of modular flavor symmetries and their phenomenology

ArXiv.org · 2025-02-17

We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group $T'$. Otherwise equivalent models based on different $T'$ lead to modular forms with different properties and, hence, produce different phenomenological features. We exemplify this in various scenarios, and show that the ability of a given model to accommodate mass and other observed hierarchies depends sensitively on the way the $T'$ is implemented.

Modular Zeros

arXiv (Cornell University) · 2025-12-24

Modular symmetries are known to be powerful and have various remarkable properties. We point out that the structure of vector-valued modular forms (VVMFs) space leads to the absence of couplings which cannot be explained in terms of the usual symmetries. These modular zeros, which correspond to gaps in spaces of VVMFs, have the power of explaining certain stringy zeros, and to explain the renowned Weinberg texture that relates the Cabibbo angle to the hierarchies of the light down and strange quarks.

Flavor Symmetries and Winding Modes

ArXiv.org · 2025-06-15

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), which underlie many modular flavor symmetries, emerge from stringy duality symmetries by orbifolding. This requires an analysis of massive states, which reveals a picture that is more intricate than the well-known situation on the torus. It involves towers of states of different quantum numbers, related by modular transformations. Members of different towers become massless at different points in moduli space. We also show that, at least in the Z_3 orbifold, the string selection rules can be understood as discrete remnants of continuous gauge symmetries. Non-Abelian discrete flavor symmetries arise as relics of various, relatively misaligned, continuous Abelian gauge symmetries. The generators of these U(1) symmetries give rise to CP-violating Clebsch-Gordan coefficients. If the modulus settles close to a critical point, the corresponding gauge bosons may be light enough to be searched for at future colliders.

Modular flavor symmetries and fermion mass hierarchies

Journal of High Energy Physics · 2025-10-03

A bstract We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus τ to be located near one of the critical points, i, i ∞, or ω . We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points i and ω . We compare the traditional Froggatt–Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries.

Flavor symmetries and winding modes

Journal of High Energy Physics · 2025-09-02 · 2 citations

A bstract 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), which underlie many modular flavor symmetries, emerge from stringy duality symmetries by orbifolding. This requires an analysis of massive states, which reveals a picture that is more intricate than the well-known situation on the torus. It involves towers of states of different quantum numbers, related by modular transformations. Members of different towers become massless at different points in moduli space. We also show that, at least in the ℤ 3 orbifold, the string selection rules can be understood as discrete remnants of continuous gauge symmetries. Non-Abelian discrete flavor symmetries arise as relics of various, relatively misaligned, continuous Abelian gauge symmetries. The generators of these U(1) symmetries give rise to $$ \mathcal{CP} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>CP</mml:mi> </mml:math> -violating Clebsch-Gordan coefficients. If the modulus settles close to a critical point, the corresponding gauge bosons may be light enough to be searched for at future colliders.

Multiple realizations of modular flavor symmetries and their phenomenology

Journal of High Energy Physics · 2025-06-11 · 2 citations

A bstract We point out that specifying the finite modular group does not uniquely fix a modular flavor symmetry. We illustrate this using the finite modular group T ′. Otherwise equivalent models based on different T ′ lead to modular forms with different properties and, hence, produce different phenomenological features. We exemplify this in various scenarios, and show that the ability of a given model to accommodate mass and other observed hierarchies depends sensitively on the way the T ′ is implemented.

Modular Flavor Symmetries and Fermion Mass Hierarchies

ArXiv.org · 2025-06-29

We investigate fermion mass hierarchies in models with modular flavor symmetries. Several key conclusions arise from the observation that the determinants of mass matrices transform as 1-dimensional vector-valued modular forms. We demonstrate that, under some fairly general assumptions, achieving hierarchical fermion masses requires the vacuum expectation value of the modulus $τ$ to be located near one of the critical points, $i$, $i\infty$, or $ω$. We also revisit the universal near-critical behavior around these points and classify the resulting mass hierarchies for the critical points $i$ and $ω$. We compare the traditional Froggatt--Nielsen mechanism with its modular variant. The knowledge and boundedness of Fourier and Taylor coefficients are crucial to the predictive power of modular flavor symmetries.

Scale-independent relations between neutrino mass parameters

ArXiv.org · 2025-11-06

Theories of flavor operate at various scales. Recently it has been pointed out that in the context of modular flavor symmetries certain combinations of observables are highly constrained, or even uniquely fixed, by modular invariance and holomorphicity. We find that even in the absence of supersymmetry these combinations are surprisingly immune against quantum corrections. This applies, in particular, to the standard model (SM) and certain 2-Higgs doublet models (2HDMs).

Heterotic Orbifold Models

arXiv (Cornell University) · 2024-01-06

We review efforts in string model building, focusing on the heterotic orbifold compactifications. We survey how one can, starting from an explicit string theory, obtain models which resemble Nature. These models exhibit the standard model gauge group, three generations of standard model matter and an appropriate Higgs sector. Unlike many unified models, these models do not suffer from problems such as doublet-triplet splitting, too rapid proton decay and the $μ$ problem. Realistic patterns of fermion masses emerge, which are partly explained by flavor symmetries, including their modular variants. We comment on challenges and open questions.