arXiv subjects

Tatsuo Kobayashi

Publications and source records attributed to Tatsuo Kobayashi.

At least 19 recordsLinked to original sources

arXiv2026

Note on arithmetic structure of modulus vacua in flux compactifications

We study modulus stabilization by background fluxes. The supersymmetric minima satisfy a holomorphic quadratic equation. As concrete examples, we consider $T^6/(\mathbb{Z}_2\times\mathbb{Z}_2')$ orientifold model and a simple Calabi-Yau compactification. The modulus values show specific patterns. For example, they show the Farey sequence. The void structure appears around modulus vacua with high degeneracies. We find a correlation between the degeneracy and the void area. The modulus vacua are related by discrete Abelian symmetries generated by the Gauss composition law, which includes the CP symmetry. Spontaneous CP violation is also discussed.

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arXiv2026

Textures of dimension-six operators in the SMEFT with non-invertible selection rules

We investigate the flavor structures of dimension-six operators in the Standard Model Effective Field Theory (SMEFT) subject to non-invertible selection rules. In particular, we classify the flavor textures of all baryon-number-conserving dimension-six SMEFT operators and determine the resulting constraints on their Wilson coefficients. The selection rules determine not only the texture zeros but also the allowed tensor structures of the Wilson coefficients, which can be expressed analytically in terms of a reduced number of independent parameters. We also find that the flavor structures of higher-dimensional operators are not necessarily aligned with those of the Yukawa couplings, in contrast to the Minimal Flavor Violation hypothesis, in which the Yukawa couplings govern the flavor structure of higher-dimensional operators. It turns out that the resulting flavor and chirality patterns differ from those typically obtained in SMEFT with conventional flavor symmetries, providing characteristic predictions for $B$-meson observables and charged-lepton-flavor-violating radiative decays.

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arXiv2026

Finite modular Coleman-Weinberg inflation

We propose a modular symmetric inflationary model based on a Coleman--Weinberg potential generated by integrating out heavy vector-like quarks that couple to the complex modulus field $τ$ through modular forms. In this framework, the imaginary part of modulus $τ$ plays the role of the inflaton, while the real part is identified with a heavy axion. We show that the model successfully explains the current cosmological observations. We further discuss reheating through modulus-dependent gauge kinetic functions and the cosmology of the axion. The axion oscillation dominates over the Universe after the reheating via inflaton decay, and then it decays before Big Bang Nucleosynthesis in the viable parameter region. The quantum fluctuation of the axion can be of order $\mathcal{O}(1)\% $ of that of the inflaton, which would induce isocurvature perturbations that may be detectable in future observations.

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arXiv2026

More about modular symmetries and non-invertible properties in magnetized compactifications

We study the modular symmetry in magnetized compactifications. The zero-modes with different Scherk-Schwarz phases transform each other. A generic model does not include modes with all the Scherk-Schwarz phases. Incomplete multiplet representations appear. Thus, the modular symmetry is violated as group-like symmetry. However, the modular symmetry still controls coupling terms in those models. Modular forms of the full symmetry appear as coupling constants.

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arXiv2026

Massive modes on magnetized blow-up manifold of $T^2/\mathbb{Z}_N$

We study massive modes on a magnetized blow-up manifold of $T^2/\mathbb{Z}_N$. The blow-up manifold can be constructed by appropriately replacing orbifold singular points with a part of $S^2$. To ensure a smooth connection between the massive modes on magnetized $T^2/\mathbb{Z}_N$ orbifold and those on magnetized $S^2$, it is required that not only the total magnetic flux as well as the total curvature but also the effective magnetic flux on the connected line remain invariant under the blow-up procedure. Furthermore, we find that the number of the localized modes at each orbifold singular point increases by one for each unit increment of the mass level.

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arXiv2026

Residual group-like symmetries in selection rules without group actions

We analyze loop-induced group-like symmetries in theories where fields are labeled by basis elements of a fusion algebra constructed from the conjugacy classes of finite groups. Although the fusion rules for conjugacy classes are in general violated at loop level, residual group-like symmetries, including both Abelian and non-Abelian ones, remain exact through a procedure referred to as ``groupification''. By examining various conjugacy classes of finite groups realized in heterotic string theory on non-Abelian orbifolds, we identify an approximate discrete symmetry that controls the magnitude of loop-induced couplings. As a result, most parameters appearing in non-invertible selection rules are natural in the sense of 't Hooft. Furthermore, we discuss anomalies of the groupification symmetry, which can impose additional constraints on models with non-invertible fusion rules.

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arXiv2026

Yukawa Textures with Enhanced Symmetries in Heterotic Calabi-Yau Compactifications

We clarify the structure of Yukawa couplings and mass matrices for matter fields in heterotic string theory on smooth Calabi-Yau threefolds with standard embedding. The topological structure of Calabi-Yau threefolds leads to interesting Yukawa textures that cannot be derived from group-theoretical symmetries, e.g., the so-called Weinberg texture in the case of two generations of matter fields. Furthermore, we find that a $U(2)$ flavor symmetry, which plays an important role in controlling higher-dimensional operators in the Standard Model effective field theory, emerges at specific loci in the moduli space of multi-Higgs fields. Small perturbations around these loci generate semi-realistic patterns of quark masses and mixings.

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arXiv2026

Zee-Babu model in a non-holomorphic modular $A_4$ symmetry and modular stabilization

We study a Zee-Babu neutrino model in a non-holomorphic modular $A_4$ symmetry, and we construct a model so that there are minimum free parameters (two complex parameters). We find only the normal hierarchy is allowed. Moreover, the allowed region to satisfy the neutrino oscillation data is localized at nearby $τ=ω$. The small absolute deviation plays a crucial role in fitting two mixings of $s^2_{23}$ and $s^2_{12}$. In addition, we obtain several predictions on Majorana and Dirac CP phases, and neutrinoless double beta decay as shown in our chi square numerical analysis. We also study modulus stabilization within the framework of non-supersymmetric models. In the end, we compute the expansion of modular forms at nearby $τ=ω$ in the Appendix so that one can apply them for a model and understand its analytical structure.

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arXiv2025

Modular weights of wave functions on magnetized torus

We study the origin of modular weights of wave functions in magnetized $T^{2}$ models. It is explicitly demonstrated that the modular weights of the wave functions on magnetized $T^2$ is equivalent to their mass level. We further extend this result to magnetized $T^{2g}$ models. As a result, we construct the wave functions of excited states in magnetized $T^{2g}$ models and show that their modular weights are likewise equivalent to the corresponding mass levels.

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arXiv2025

Generalized CP from non-invertible selection rules

We study a framework in which fields are labeled by basis elements of a fusion algebra with non-invertible fusion rules. In particular, we consider the case where fields are labeled by conjugacy classes of a finite group rather than its irreducible representations. When the fusion rules possess a $\mathbb{Z}_2$ symmetry identified with charge conjugation, a CP-invariant system can be consistently defined together with parity transformation. Furthermore, it is found that combining group-based flavor symmetries underlying non-invertible selection rules with CP symmetry naturally leads to a generalized CP transformation. We also demonstrate the possibility of spontaneous CP violation in this framework and discuss its implications for Yukawa textures.

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arXiv2025

Radiative neutrino mass models from non-invertible selection rules

We apply non-invertible selection rules coming from a fusion algebra to radiative neutrino mass models where fields are labeled by the elements in the algebra. Since non-invertible selection rules only hold at tree level, radiative corrections naturally explain the origin of tiny neutrino masses. Furthermore, a remnant symmetry of the fusion algebra protects the stability of dark matter, which is conventionally imposed in radiative neutrino models. We also find that interesting neutrino mass textures are realized by assigning fields to family-dependent elements in the algebra.

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arXiv2025

GUT-motivated non-invertible symmetry as a solution to the strong CP problem and the neutrino CP-violating phase

The unsuppressed CP violation in QCD is a problem in the standard model. If we have some mechanism to guarantee real determinants of the quark mass matrices, the vanishing physical vacuum angle $\bar θ$ indicates the CP invariance at the fundamental level. Thus, the small ${\bar θ}$ is technically natural, since we have an enhanced CP symmetry in the limit of the vanishing $\bar θ=0$. In fact, it was proved that the vacuum angle is never renormalized up to the four-loop level once it is fixed at 0 value at some high energy scale. The purpose of this paper is to construct a model which guarantees the real determinants of the quark mass matrices assuming a non-invertible symmetry.

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arXiv2025

Non-Invertible Selection Rules on Heterotic Non-Abelian Orbifolds

We investigate coupling selection rules in heterotic string theory on non-Abelian orbifolds. Since boundary conditions on the orbifolds are classified by conjugacy classes of space group elements, non-Abelian orbifolds give rise to non-invertible selection rules on couplings among twisted sectors as well as ones including untwisted sectors. Furthermore, we find that non-invertible selection rules lead to characteristic patterns of Yukawa matrices.

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arXiv2025

Coupling Selection Rules in Heterotic Calabi-Yau Compactifications

We study coupling selection rules of chiral matter fields in heterotic string theory with standard embedding. These selection rules are determined by topological properties of Calabi-Yau threefolds. We classify coupling selection rules on complete intersection Calabi-Yau threefolds for $h^{1,1}\leq 5$. It is found that all of these selection rules for $h^{1,1}\leq 5$ are understood by combinations of only five types of fusion rules.

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arXiv2025

Lepton mass textures from non-invertible multiplication rules

We study the lepton mass textures, which are derived by $\mathbb{Z}_2$ gauging of $\mathbb{Z}_M$ symmetries. We can obtain various textures for the Yukawa couplings in the charged lepton sector, but the patterns of neutrino mass matrices are limited. All the obtained textures can not be realized by group-theoretical symmetries, and certain textures can lead to realistic results.

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arXiv2025

Classification of Modular Symmetries in Type IIB Flux Landscape

In this work, we study modular symmetries in type IIB flux landscape by investigating symplectic basis transformations of period vectors on toroidal orbifolds. To fix explicit cycles of a third-cohomology basis regarding the untwisted complex structure modulus, which is necessary to construct the period vectors, we find that the following two symmetries are required for the period vectors: (i) ``Scaling duality '' which is a generalized $S$-transformation of $PSL(2, \mathbb{Z})$ and (ii) the modular symmetries to be consistent with symmetries derived from mass spectra of the closed string in type IIB string theory. Furthermore, by considering flux quanta on the cycles, we explore type IIB flux vacua on toroidal orientifolds and flux transformations under the modular symmetries of the period vectors.

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arXiv2025

Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model

We propose a three-zero texture for the down-quark mass matrix within a $SU(5)$ GUT-inspired Standard Model, enforced by a non-invertible selection rule originating from $\mathbb{Z}_2$ gauging of $\mathbb{Z}_N$ symmetries. Assuming CP invariance at the high-energy scale, our framework solves the strong CP problem while reproducing a realistic quark mass matrix. The CP symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields $η_i$, which generate the CP phase in the CKM matrix without inducing the QCD $\barθ$ term. The present model incorporates three generations of matter, Higgs, and additional scalars with a common structure under the non-invertible symmetry, which may be naturally embedded into $SO(10)$ GUTs at high energies.

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arXiv2025

Stringy Constraints on Modular Flavor Models

We investigate stringy constraints on moduli spaces in modular flavor models by analyzing moduli-dependent threshold corrections in heterotic string vacua. While moduli play a crucial role in determining the flavor structure of fermions predicted by modular flavor models, the parameter space in which their vacuum expectation values are allowed has not been fully explored. In this work, within the framework of perturbative heterotic string theory on toroidal orbifolds, we derive constraints on the moduli space and study their systematic behavior. We characterize the stringy constraints in terms of the dilaton, the beta-function coefficients, and the ratio between a complex-structure modulus and a Kähler modulus. It is found that the large value of the modulus controlling the flavor structure, i.e., $τ\simeq i \infty$, lies in the Swampland, and the self-dual point $τ=i$ is also disfavored in the large volume regime of toroidal backgrounds. In addition, we discuss the phenomenological implications of these stringy constraints.

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