arXiv subjects

Keiya Ishiguro

Publications and source records attributed to Keiya Ishiguro.

15 recordsLinked to original sources

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

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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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

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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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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arXiv2022

Residual flavor symmetry breaking in the landscape of modular flavor models

We study a symmetry breaking of residual flavor symmetries realized at fixed points of the moduli space. In the supersymmetric modular invariant theories, a small departure of the modulus from fixed points is required to realize fermion mass hierarchies and sizable CP-breaking effects. We investigate whether one can dynamically fix the moduli values in the vicinity of the fixed points in the context of Type IIB string theory. It is found that the string landscape prefers $|δτ| \simeq 10^{-5}$ for the deviation of the complex structure modulus from all fixed points and the CP-breaking vacuum is statistically favored. To illustrate phenomenological implications of distributions of moduli values around fixed points, we analyze the lepton sector on a concrete $A_4$ modular flavor model.

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arXiv2022

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 $Sp(2h+2, \mathbb{C})$ modular symmetries of Calabi-Yau threefolds with $h$ being the number of moduli fields. Together with the $\mathbb{Z}_2^{\rm CP}$ CP symmetry, they are enhanced to $GSp(2h+2, \mathbb{C})\simeq Sp(2h+2, \mathbb{C})\rtimes \mathbb{Z}_2^{\rm CP}$ generalized symplectic modular symmetry. We exemplify the $S_3, S_4, T^\prime, S_9$ non-Abelian flavor symmetries on explicit toroidal orbifolds with and without resolutions and $\mathbb{Z}_2,S_4$ 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 threefolds. These flavor symmetries are further enlarged to non-Abelian discrete groups by the CP symmetry.

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arXiv2021

Sharpening the Boundaries Between Flux Landscape and Swampland by Tadpole Charge

We investigate the vacuum structure of four-dimensional effective theory arising from Type IIB flux compactifications on a mirror of the rigid Calabi-Yau threefold, corresponding to a T-dual of the DeWolfe-Giryavets-Kachru-Taylor model in Type IIA flux compactifications. By analyzing the vacuum structure of this interesting corner of string landscape, it turns out that there exist perturbatively unstable de Sitter (dS) vacua in addition to supersymmetric and non-supersymmetric anti-de Sitter vacua. On the other hand, the stable dS vacua appearing in the low-energy effective action violate the tadpole cancellation condition, indicating a strong correlation between the existence of dS vacua and the flux-induced D3-brane charge (tadpole charge). We also find analytically that the tadpole charge constrained by the tadpole cancellation condition emerges in the scalar potential in a nontrivial way. Thus, the tadpole charge would restrict the existence of stable dS vacua, and this fact underlies the statement of the dS conjecture. Furthermore, our analytical and numerical results exhibit that distributions of ${\cal O}(1)$ parameters in expressions of several swampland conjectures peak at specific values.

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arXiv2021

Spontaneous CP violation and symplectic modular symmetry in Calabi-Yau compactifications

We explore the geometrical origin of CP and the spontaneous CP violation in Calabi-Yau compactifications. We find that the CP symmetry is identified with an outer automorphism of the symplectic modular group in the large complex structure regime of Calabi-Yau threefolds, thereby enlarging the symplectic modular group to their semidirect product group. The spontaneous CP violation is realized by the introduction of fluxes, whose effective action is invariant under CP as well as the discrete $\mathbb{Z}_2$ symmetry or $\mathbb{Z}_4$ R-symmetry. We explicitly demonstrate the spontaneous CP violation on a specific Calabi-Yau threefold.

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arXiv2021

Hierarchical structure of physical Yukawa couplings from matter field Kähler metric

We study the impacts of matter field Kähler metric on physical Yukawa couplings in string compactifications. Since the Kähler metric is non-trivial in general, the kinetic mixing of matter fields opens a new avenue for realizing a hierarchical structure of physical Yukawa couplings, even when holomorphic Yukawa couplings have the trivial structure. The hierarchical Yukawa couplings are demonstrated by couplings of pure untwisted modes on toroidal orbifolds and their resolutions in the context of heterotic string theory with standard embedding. Also, we study the hierarchical couplings among untwisted and twisted modes on resolved orbifolds.

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arXiv2020

Landscape of Modular Symmetric Flavor Models

We study the moduli stabilization from the viewpoint of modular flavor symmetries. We systematically analyze stabilized moduli values in possible configurations of flux compactifications, investigating probabilities of moduli values and showing which moduli values are favorable from our moduli stabilization. Then, we examine their implications on modular symmetric flavor models. It is found that distributions of complex structure modulus $τ$ determining the flavor structure are clustered at a fixed point with the residual $\mathbb{Z}_3$ symmetry in the $SL(2,\mathbb{Z})$ fundamental region. Also, they are clustered at other specific points such as intersecting points between $|τ|^2=k/2$ and ${\rm Re}\,τ=0,\pm 1/4, \pm1/2$, although their probabilities are less than the $\mathbb{Z}_3$ fixed point. In general, CP-breaking vacua in the complex structure modulus are statistically disfavored in the string landscape. Among CP-breaking vacua, the values ${\rm Re}\,τ=\pm 1/4$ are most favorable in particular when the axio-dilaton $S$ is stabilized at ${\rm Re}\,S=\pm 1/4$. That shows a strong correlation between CP phases originated from string moduli.

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