arXiv subjects

Hajime Otsuka

Publications and source records attributed to Hajime Otsuka.

At least 55 records · Page 3Linked to original sources

arXiv2024

Spontaneous CP violation and partially broken modular flavor symmetries

We study the realization of spontaneous CP violation through moduli stabilization. In modular flavor models, the source of CP violation is the vacuum expectation values of the complex structure moduli of toroidal compact space. We demonstrate that the combined effects of Type IIB flux compactifications with modular invariant couplings between the moduli and matter fields can induce spontaneous CP violation without or with supersymmetry breaking. Furthermore, some general properties of CP and modular invariant scalar potentials are presented. It is found that certain modifications or partial breakings of modular symmetry are useful in generating spontaneous CP violation.

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arXiv2024

Yukawa textures from non-invertible symmetries

Phenomenological aspects of non-invertible symmetries, in particular the flavor structure of quarks and leptons, are studied. We start with a $\mathbb{Z}_M$ discrete symmetry and gauge $\mathbb{Z}_2$ so as to obtain a non-invertible symmetry. We study which Yukawa textures can be derived from the non-invertible symmetries. Various textures can be realized and some of them cannot be realized by a conventional symmetry. For example, the nearest neighbor interaction texture as well as other interesting textures of quarks and leptons are obtained.

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arXiv2024

Flavor symmetries from modular subgroups in magnetized compactifications

We study the flavor structures of zero-modes, which are originated from the modular symmetry on $T^2_1\times T^2_2$ and its orbifold with magnetic fluxes. We introduce the constraint on the moduli parameters by $τ_2=Nτ_1$, where $τ_i$ denotes the complex structure moduli on $T^2_i$. Such a constraint can be derived from the moduli stabilization. The modular symmetry of $T^2_1 \times T^2_2$ is $SL(2,\mathbb{Z})_{τ_1} \times SL(2,\mathbb{Z})_{τ_2} \subset Sp(4,\mathbb{Z})$ and it is broken to $Γ_0(N) \times Γ^0(N)$ by the moduli constraint. The wave functions represent their covering groups. We obtain various flavor groups in these models.

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arXiv2024

Nambu-Goldstone Modes in Magnetized $T^{2n}$ Extra Dimensions

We consider a $U(1)$ gauge theory on $M^4\times T^4$ with background magnetic fluxes. We show that a theory including arbitrary fluxes can always be studied in a theory involving only diagonal fluxes by appropriate coordinate transformations. It is found that the number of independent magnetic fluxes is equal to the rank of the classical value of the field strength matrix, ${\rm rank}\langle F\rangle$. The number of massless zero modes induced from extra components of higher-dimensional gauge field (Wilson-line scalar field), is also determined by ${\rm rank}\langle F\rangle$. We explicitly confirm that the quantum corrections due to the matter fermion to the squared mass of Wilson-line scalar field cancel out at one-loop level. For this purpose, we derive the fermion mass spectrum on $M^4\times T^4$ with arbitrary fluxes. By taking the flux diagonal basis, creation and annihilation operators for Kaluza-Klein quantum numbers are defined appropriately. Our results are easily generalized to the case of $M^4\times T^{2n}~(n\geq3)$.

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arXiv2024

Stringy constraints on primordial electromagnetic fields in axion inflation

We study primordial electromagnetic fields in effective actions of string theory. In contrast to a conventional scenario of producing primordial electromagnetic fields induced by the axion inflation, we deal with the Dirac-Born-Infeld action as a non-linear generation of Maxwell theory. It turns out that the intensity of generated electromagnetic fields is bounded from above by the string scale which can also be rewritten in terms of supersymmetry breaking scale in the context of type IIB Large Volume Scenario. The instability parameter $ξ$ is constrained by the tadpole cancellation condition of D3-branes and a realization of hierarchy between the string scale and the Hubble scale of inflation. Hence, the magnetogenesis can be realized in the limited corner of the string landscape due to the ${\cal O}(1)$ value of the coefficient of Chern-Simons coupling.

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arXiv2024

Induced moduli oscillation by radiation and space expansion in a higher-dimensional model

We investigate the cosmological expansion of the 3D space in a 6D model compactified on a sphere, beyond the 4D effective theory analysis. We focus on a case that the initial temperature is higher than the compactification scale. In such a case, the pressure for the compact space affects the moduli dynamics and induces the moduli oscillation even if they are stabilized at the initial time. Under some plausible assumptions, we derive the explicit expressions for the 3D scale factor and the moduli background in terms of analytic functions. Using them, we evaluate the transition times between different cosmological eras as functions of the model parameters and the initial temperature.

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arXiv2024

Modular forms and hierarchical Yukawa couplings in heterotic Calabi-Yau compactifications

We study the modular symmetry in heterotic string theory on Calabi-Yau threefolds. In particular, we examine whether moduli-dependent holomorphic Yukawa couplings are described by modular forms in the context of heterotic string theory with standard embedding. We find that $SL(2,\mathbb{Z})$ modular symmetry emerges in asymptotic regions of the Calabi-Yau moduli space. The instanton-corrected holomorphic Yukawa couplings are then given by modular forms under $SL(2,\mathbb{Z})$ or its congruence subgroups such as $Γ_0(3)$ and $Γ_0(4)$. In addition to the modular symmetry, it turns out that another coupling selection rule controls the structure of holomorphic Yukawa couplings. Furthermore, the coexistence of both the positive and negative modular weights for matter fields leads to a hierarchical structure of matter field Kähler metric. Thus, these holomorphic modular forms and the matter field Kähler metric play an important role in realizing a hierarchical structure of physical Yukawa couplings.

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arXiv2024

Upper bound on the Atiyah-Singer index from tadpole cancellation

We propose an upper bound on the Atiyah-Singer index in the effective action of string theory. For $E_8 \times E_8^\prime$ and $SO(32)$ heterotic string theories on smooth Calabi-Yau threefolds with line bundles, we find that the tadpole cancellation and supersymmetry conditions lead to an upper bound on the generation number of quarks and leptons as well as Higgs doublets. By taking into account the observed value of four-dimensional gauge couplings and the supergravity approximation, we explicitly evaluate the bound on favorable complete intersection Calabi-Yau threefolds. The bound can be extended to Calabi-Yau threefolds in the Kreuzer-Skarke database. We also put the upper bound on the Atiyah-Singer index in Type IIB/F-theory compactifications.

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arXiv2024

Exploring the flavor structure of quarks and leptons with reinforcement learning

We propose a method to explore the flavor structure of quarks and leptons with reinforcement learning. As a concrete model, we utilize a basic value-based algorithm for models with $U(1)$ flavor symmetry. By training neural networks on the $U(1)$ charges of quarks and leptons, the agent finds 21 models to be consistent with experimentally measured masses and mixing angles of quarks and leptons. In particular, an intrinsic value of normal ordering tends to be larger than that of inverted ordering, and the normal ordering is well fitted with the current experimental data in contrast to the inverted ordering. A specific value of effective mass for the neutrinoless double beta decay and a sizable leptonic CP violation induced by an angular component of flavon field are predicted by autonomous behavior of the agent. Our finding results indicate that the reinforcement learning can be a new method for understanding the flavor structure.

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arXiv2023

Flavor, CP and Metaplectic Modular Symmetries in Type IIB Chiral Flux Vacua

We examine symmetries of chiral four-dimensional vacua of Type IIB flux compactifications with vanishing superpotential $W=0$. We find that the ${\cal N}=1$ supersymmetric MSSM-like and Pati-Salam vacua possess enhanced discrete symmetries in the effective action below the mass scale of stabilized complex structure moduli and dilaton. Furthermore, a generation number of quarks/leptons is small on these vacua where the flavor, CP and metaplectic modular symmetries are described in the framework of eclectic flavor symmetry.

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arXiv2023

Autoencoder-Driven Clustering of Intersecting D-brane Models via Tadpole Charge

We study the well-known type IIA intersecting D-brane models on the $T^6/(\mathbb{Z}_2 \times \mathbb{Z}'_2)$ orientifold via a machine-learning approach. We apply several autoencoder models with and without positional encoding to the D6-brane configurations satisfying certain concrete models described in arXiv:hep-th/0510170 and attempt to extract some features which the configurations possess. We observe that the configurations cluster in two-dimensional latent layers of the autoencoder models and analyze which physical quantities are relevant to the clustering. As a result, it is found that tadpole charges of hidden D6-branes characterize the clustering. We expect that there is another important factor because a checkerboard pattern in two-dimensional latent layers is observed in the clustering.

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arXiv2023

Flux Landscape with Enhanced Symmetry Not on $SL(2, \mathbb{Z})$ Elliptic Points

We study structures of solutions for SUSY Minkowski F-term equations on two toroidal orientifolds with $h^{2, 1} = 1$. Following our previous study \cite{Ishiguro:2020tmo}, with fixed upper bounds of a flux D3-brane charge $N_{\rm flux}$, we obtain a whole Landscape and a distribution of degeneracies of physically-distinct solutions for each case. In contrast to our previous study, we consider a non-factorizable toroidal orientifold and its Landscape on which $SL(2, \mathbb{Z})$ is violated into a certain congruence subgroup, as it had been known in past studies. We find that it is not the entire duality group that a complex-structure modulus $U$ enjoys but its outer semi-direct product with a "scaling" outer automorphism group. The fundamental region is enlarged to include the $|U| < 1$ region. In addition, we find that high degeneracy is observed at an elliptic point, not of $SL(2, Z)$ but of the outer automorphism group. Furthermore, $\mathbb{Z}_2$-enhanced symmetry is realized on the elliptic point. The outer automorphism group is exceptional in the sense that it is consistent with a symplectic basis transformation of background three-cycles, as opposed to the outer automorphism group of $SL(2, \mathbb{Z})$. We also compare this result with Landscape of another factorizable toroidal orientifold.

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arXiv2023

Novel moduli space in modular flavor models : a case study for modular $T'$ seesaw model with hidden $SU(2)$ gauge symmetry

We study flavor phenomenologies in a basis of a double covering of modular $A_4$ group with a hidden $SU(2)$ symmetry, in which we work on regions at nearby two fixed points and three special points. These special points of $SL(2,\mathbb{Z})$ moduli space are statistically favored in flux compactifications of Type IIB string theory. Neutrino masses are approximately obtained by using the seesaw mechanism due to our two additional symmetries. We perform chi square numerical analysis for each of the fixed/special points in the normal and inverted hierarchies and demonstrate predictions for each case. Then, we briefly discuss the possible signature of hidden gauge bosons at collider experiments from the hidden $SU(2)$ symmetry.

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arXiv2023

Modular flavor models with positive modular weights: a new lepton model building

We propose an interesting assignment of positive modular wights for fields in a modular non-Abelian discrete flavor symmetry. By this assignment, we can construct inverse seesaw and linear seesaw models without any additional symmetries which possess good testability in current experiments. At first, we discuss probabilities for positive modular wights from a theoretical point of view. Then we show concrete examples of inverse seesaw and linear seesaw scenarios applying modular $A_4$ symmetry as examples and demonstrate some predictions as well as being consistent with experimental results such as their masses and mixings.

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arXiv2023

Texture zeros realization in a three-loop radiative neutrino mass model from modular $A_4$ symmetry

We derive verifiable two-zero textures in the framework of a three-loop induced neutrino mass model applying a modular $A_4$ symmetry for the lepton sector. Interestingly, the neutrino mass structure is determined by assignments of the right-handed charged-lepton particles only. We show all the possible texture patterns and demonstrate their analytical and numerical analyses. Finally, we mention a possibility of detection for doubly-charged boson via colliders that decays into specific modes due to the flavor symmetry.

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arXiv2023

Sequestered String Models imply Split Supersymmetry

Sequestering is a promising mechanism in 4D string models to reconcile high-scale inflation with low-energy supersymmetry. In this scenario the MSSM lives on branes at singularities and it is sequestered from the sources of supersymmetry breaking in the bulk. The soft-terms are suppressed with respect to the gravitino mass so that all moduli are heavy enough to avoid any cosmological moduli problem. In this paper we study stability bounds and flavour constraints on sequestered string models, finding that they can be satisfied if the soft-terms give rise to a mass spectrum typical of split supersymmetry with TeV-scale gauginos and sfermions around $10^7$ GeV. When instead scalar and gaugino masses are of the same order of magnitude, large flavour changing neutral currents can be avoided only by pushing the soft-terms above $10^6$ GeV. However this scenario is in tension with stability bounds due to the presence of charge and colour breaking vacua which could be populated in the early universe, and the possible emergence of directions along which the potential is unbounded from below.

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arXiv2023

Moduli inflation from modular flavor symmetries

We study slow-roll inflation model controlled by the modular flavor symmetry. In the model, the modulus field plays a role of inflaton and the introduction of the stabilizer field coupled to a modular form in the superpotential produces the inflaton potential. In order to generate the flat direction for the slow-roll inflation, we consider the Kähler potential corrected by the modular form. It is noted that the modulus field perpendicular to the inflaton direction is stabilized during the inflation. The model turns out to be consistent with the current observations and behaves similarly to the $α$-attractor models in some parameter spaces. The inflaton rolls down to the CP-symmetric vacuum at the end of inflation.

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arXiv2023

Remark on modular weights in low-energy effective field theory from type II string theory

We revisit the modular weights in type IIB magnetized D-brane models. The simple analysis of wave function shows that the four-dimensional matter fields have the modular weight -1/2, but it may shift as one in type IIA intersecting D-brane models. For example, the localized gauge flux as well as the localized curvature can shift the modular weight in the magnetized D-brane models. Such corrections do not affect physical couplings such as physical Yukawa couplings. However, it leads to differences in supersymmetry breaking sfermion masses, which depend on the modular weights, although the $A$-term coefficients and the sum of sfermion masses squared seem to be the same between two models.

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