arXiv subjects

Hajime Otsuka

Publications and source records attributed to Hajime Otsuka.

At least 37 records · Page 2Linked to original sources

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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arXiv2025

Inflationary constraints on the moduli-dependent species scale in modular invariant theories

We demonstrate that a broad class of modular inflation models predicts the emergence of new physics within an energy range of approximately $ 10^{15} \, \mathrm{GeV} $ to $ 10^{17} \, \mathrm{GeV} $. This prediction arises by comparing the moduli-dependent species scale with observational constraints on inflation. Specifically, we illustrate this within the context of $ SL(2, \mathbb{Z}) $-modular inflation models by re-expressing inflationary observables in terms of the species scale. We further discuss the implications of this approach for generic Calabi-Yau threefolds.

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arXiv2025

Higgs-Modular Inflation

We investigate the role of the Higgs field as a fundamental scalar in the Standard Model within the framework of modular inflation models, where a modulus field acts as the inflaton and its interactions are governed by an underlying modular symmetry. In general, the Higgs field can participate in the dynamics of modular inflation, leading to a two-field inflationary system-termed \emph{Higgs-Modular inflation}-which exhibits non-trivial dynamics and interesting phenomenological implications. We analyze Higgs-Modular inflation both analytically and numerically, highlighting its attractor behavior and the resulting observational constraints. In particular, we find that Higgs-Modular inflation is favored by the latest data release from the Atacama Cosmology Telescope (ACT) in certain regions of parameter space. This is in contrast to both pure Higgs inflation and pure modular inflation with a Starobinsky-type potential, which tend to predict a relatively low spectral index. Additionally, we discuss the cutoff scale of this inflationary model and the reheating processes induced by the decays of the modulus and the Higgs field.

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arXiv2025

On discrete gauging and non-invertible selection rules

We clarify selection rules of conjugacy classes of several finite discrete groups where we deal with both gauged and ungauged cases. We find that the selection rules enjoy finite Abelian or non-Abelian discrete symmetries originating from the inner and/or outer automorphism of underlying discrete groups. Since the selection rules of conjugacy classes do not obey conventional group-like selection rules, they open up new coupling selection rules of fields which are labeled by the conjugacy classes.

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arXiv2025

Matter symmetries in supersymmetric standard models from non-invertible selection rules

We discuss phenomenological implications of non-invertible selection rules in the framework of the supersymmetric standard model. We find that a remnant $\mathbb{Z}_2$ symmetry of fusion algebras which holds at all-loop order plays the role of $R$-parity, forbidding baryon and lepton violating operators. In addition, a combination of Standard Model gauge symmetry and the non-invertible selection rules lead to baryon triality and proton hexality that can protect the proton from decay. In general, our finding selection rules can not realize the same results as conventional $\mathbb{Z}_N$ symmetries in the supersymmetric standard model. We also clarify the assignments of matter fields under the fusion algebras that are consistent with $SU(4) \times SU(2) \times SU(2)$, $SU(5)$, and $SO(10)$ grand unified theories.

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arXiv2025

More about quark Yukawa textures from selection rules without group actions

We study the coupling selection rules associated with non-group symmetries, i.e., $\mathbb{Z}_2$ gauging of $\mathbb{Z}_M$ symmetries. We clarify which Yukawa textures can be derived by our selection rules for $M=3, 4$, and 5, and obtain various textures including the the nearest neighbor interaction type and its extension. Some of them cannot be realized by a conventional group-like symmetry. They lead to interesting phenomenology such as a solution to the strong CP problem without axion.

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arXiv2025

Response of Kaluza-Klein mass spectrum to deformations of rugby-ball compact space

We investigate the response of the Kaluza-Klein (KK) mass spectrum to various deformations of the rugby-ball background in 6-dimensional supergravity. We derived the mode equations that contain the 3-dimensional scale factor and the lapse function. By solving these, we numerically evaluate the KK masses for a bulk scalar and a spinor when the background has a nontrivial dependence on the position in the compact space. We clarify some qualitative features of the spectrum deformation for some perturbations of the rugby-ball background. For perturbations of a supersymmetric background, we find that the mass-splitting between bosonic and fermionic modes is much smaller than the deviation from the values of the supersymmetric mass eigenvalues.

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arXiv2025

Classification of Modular Symmetries in Non-Supersymmetric Heterotic String theories

We study modular symmetries in non-supersymmetric heterotic string theories on toroidal backgrounds with Wilson line modulus, constructed by stringy Scherk-Schwartz compactification. In particular, we focus on a subgroup of the T-duality group $O(D+16,D,\mathbb{Z})$ with $D=2$ given by an outer automorphism of the Narain lattice, which can be mapped to the Siegel modular group $\mathrm{Sp}(4,\mathbb{Z})$. We classify the modular symmetries and a $CP$-like symmetry on $T^2$ and its orbifolds with symmetric and asymmetric orbifold twists. It turns out that the non-supersymmetric heterotic string theories only enjoy a part of modular symmetries in contrast to supersymmetric ones. Furthermore, the gauge symmetry is maximally enhanced at fixed points of modular symmetries on $T^2$ on which we analyze the vacuum structure of eight-dimensional tachyon-free vacua.

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arXiv2025

Modular symmetry of localized modes

We study the modular symmetry of localized modes on fixed points of $T^2/\mathbb{Z}_2$ orbifold. First, we find that the localized modes with even (odd) modular weight generally have $Δ(6n^2)$ ($Δ'(6n^2)$) modular flavor symmetry. Moreover, when we consider an additional Ansatz, the localized modes with even (odd) modular weight generally enjoy $S_3$ ($S'_4$) modular flavor symmetry, and we show the concrete wave functions of the localized modes.

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arXiv2024

Quantum aspects of non-invertible flavor symmetries in intersecting/magnetized D-brane models

We discuss selection rules of chiral matters in type IIA intersecting and IIB magnetized D-brane models on toroidal orbifolds. Since the chiral matters on toroidal orbifolds are labeled by a certain conjugacy class of the gauged orbifold group, the selection rules involve non-trivial fusion rules. We find that the representation of the chiral matters is described by a $D_4$ flavor symmetry for an even number of magnetic fluxes or winding numbers at tree level. Furthermore, the $D_4$ symmetry still remains even when we take into account loop effects. We also study non-perturbative effects such as D-brane instantons.

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arXiv2024

Non-invertible flavor symmetries in magnetized extra dimensions

We discuss non-invertible symmetries in toroidal compactifications of higher dimensional Yang-Mills theory with magnetic fluxes, which can be regarded as an effective action of type IIB string theory with magnetized D-branes. Specifically, we derive fusion rules of discrete isometry operators, which are invariant under the $\mathbb{Z}_N$ orbifold twist. It turns out that degenerate chiral zero-modes non-trivially transform under the non-invertible symmetries in the context of quantum mechanics. Hence, non-invertible symmetries correspond to flavor symmetries of chiral zero modes and determine their flavor structure. We explicitly show the representations and selection rules of chiral zero modes on their wave functions. These zero modes may correspond to generations of quarks and leptons in four-dimensional low-energy effective field theory.

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arXiv2024

Stabilization of a twisted modulus on a mirror of rigid Calabi-Yau manifold

We study the stabilization of a twisted modulus in Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold. By analyzing the effective action of twisted and untwisted moduli, we find that three-form fluxes satisfying the tadpole cancellation conditions lead to supersymmetric AdS vacua. We also investigate swampland conjectures on this non-geometric background.

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arXiv2024

Moduli stabilization and light axion by Siegel modular forms

We discuss the stabilization of multiple moduli by utilizing Siegel modular forms in the framework of $Sp(2g,\mathbb{Z})$ modular invariant theories. We derive the stationary conditions at CP-conserving fixed points for a generic modular- and CP-invariant scalar potential. The stabilization of multiple moduli is explicitly demonstrated in $Sp(4,\mathbb{Z})$ and $Sp(6,\mathbb{Z})$ modular invariant scalar potentials. Furthermore, it turns out that there exists a light axion when the moduli are stabilized nearby a fixed point.

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