Hikaru Uchida

Hokkaido University

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Hikaru Uchida has a total of 21 co-authors. Here are the top co-authors by number of shared publications:

Tatsuo Kobayashi
Hokkaido University Department of Physics Sapporo 060-0810
17 shared publications
Hajime Otsuka
Kyushu University
10 shared publications
Kaito Nasu
Hokkaido University
7 shared publications
Shota Kikuchi
Department of Physics, Hokkaido University, Sapporo, Japan
6 shared publications
Maki Takeuchi
Yamaguchi University
4 shared publications
Shohei Takada
Hokkaido University
4 shared publications

Latest Publications

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- 4 May 2026
- Published by Springer Nature in Journal of High Energy Physics
Modular weights of wave functions on magnetized torus
by Tim Jeric, Tatsuo Kobayashi, Hajime Otsuka, Maki Takeuchi, Hikaru Uchida
A bstract: 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 are equivalent to their mass level. We further extend this result to magnetized T ^{2
g} models. As a result, we construct the wave functions of excited states in magnetized T ^{2
g} models and show that their modular weights are likewise equivalent to the corresponding mass levels.
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- 4 May 2026
- Published by Springer Nature in Journal of High Energy Physics
Open Access
Modular weights of wave functions on magnetized torus
by Tim Jeric, Tatsuo Kobayashi, Hajime Otsuka, Maki Takeuchi, Hikaru Uchida
A bstract: 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 are equivalent to their mass level. We further extend this result to magnetized T ^{2
g} models. As a result, we construct the wave functions of excited states in magnetized T ^{2
g} models and show that their modular weights are likewise equivalent to the corresponding mass levels.
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Cited by 3
- 12 December 2024
- Published by American Physical Society (APS) in Physical Review D
Modular symmetry of localized modes
by Tatsuo Kobayashi, Hajime Otsuka, Shohei Takada, Hikaru Uchida
We study the modular symmetry of localized modes on fixed points of T 2 / Z 2 orbifold. First, we find that the localized modes with even (odd) modular weight generally have Δ ( 6 n 2 ) [ Δ ′ ( 6 n 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. Published by the American Physical Society 2024
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- 12 December 2024
- Published by American Physical Society (APS) in Physical Review D
Open Access
Modular symmetry of localized modes
by Tatsuo Kobayashi, Hajime Otsuka, Shohei Takada, Hikaru Uchida
We study the modular symmetry of localized modes on fixed points of T 2 / Z 2 orbifold. First, we find that the localized modes with even (odd) modular weight generally have Δ ( 6 n 2 ) [ Δ ′ ( 6 n 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. Published by the American Physical Society 2024
Cited by 3
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Cited by 19
- 10 April 2024
- Published by Springer Nature in Journal of High Energy Physics
Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $\widetilde{\Delta }\left(96\right)$
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study an approach to construct Siegel modular forms from Sp(6, Z). Zero-mode wave functions on T ⁶ with magnetic flux background behave Siegel modular forms at the origin. Then T-symmetries partially break depending on the form of background magnetic flux. We study the background such that three T-symmetries T _I, T _II and T _III as well as the S-symmetry remain. Consequently, we obtain Siegel modular forms with three moduli parameters (ω ₁, ω ₂, ω ₃), which are multiplets of finite modular groups. We show several examples. As one of examples, we study Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$ in detail. Then, as a phenomenological applicantion, we study quark flavor models using Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$ . Around the cusp, ω ₁ = i∞, the Siegel modular forms have hierarchical values depending on their T _I-charges. We show the deviation of ω ₁ from the cusp can generate large quark mass hierarchies without fine-tuning. Furthermore CP violation is induced by deviation of ω ₂ from imaginary axis.
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- 10 April 2024
- Published by Springer Nature in Journal of High Energy Physics
Open Access
Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $\widetilde{\Delta }\left(96\right)$
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study an approach to construct Siegel modular forms from Sp(6, Z). Zero-mode wave functions on T ⁶ with magnetic flux background behave Siegel modular forms at the origin. Then T-symmetries partially break depending on the form of background magnetic flux. We study the background such that three T-symmetries T _I, T _II and T _III as well as the S-symmetry remain. Consequently, we obtain Siegel modular forms with three moduli parameters (ω ₁, ω ₂, ω ₃), which are multiplets of finite modular groups. We show several examples. As one of examples, we study Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$ in detail. Then, as a phenomenological applicantion, we study quark flavor models using Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$ . Around the cusp, ω ₁ = i∞, the Siegel modular forms have hierarchical values depending on their T _I-charges. We show the deviation of ω ₁ from the cusp can generate large quark mass hierarchies without fine-tuning. Furthermore CP violation is induced by deviation of ω ₂ from imaginary axis.
Cited by 19
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Cited by 25
- 11 March 2024
- Published by American Physical Society (APS) in Physical Review D
Modular symmetry in magnetized $T^{2 g}$ torus and orbifold models
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study the modular symmetry in magnetized $T^{2 g}$ torus and orbifold models. The $T^{2 g}$ torus has the modular symmetry $Γ_{g} = S p (2 g, Z)$ . The magnetic flux background breaks the modular symmetry to a certain normalizer $N_{g} (H)$ . We classify remaining modular symmetries by magnetic flux matrix types. Furthermore, we study the modular symmetry for wave functions on the magnetized $T^{2 g}$ and certain orbifolds. It is found that wave functions on magnetized $T^{2 g}$ as well as its orbifolds behave as the Siegel modular forms of weight $1 / 2$ and ${\tilde{N}}_{g} (H, h)$ , which is the metaplectic congruence subgroup of the double covering group of $N_{g} (H)$ , ${\tilde{N}}_{g} (H)$ . Then, wave functions transform nontrivially under the quotient group, ${\tilde{N}}_{g, h} = {\tilde{N}}_{g} (H) / {\tilde{N}}_{g} (H, h)$ , where the level $h$ is related to the determinant of the magnetic flux matrix. Accordingly, the corresponding four-dimensional chiral fields also transform nontrivially under ${\tilde{N}}_{g, h}$ modular flavor transformation with modular weight $- 1 / 2$ . We also study concrete modular flavor symmetries of wave functions on magnetized $T^{2 g}$ orbifolds.
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- 11 March 2024
- Published by American Physical Society (APS) in Physical Review D
Open Access
Modular symmetry in magnetized $T^{2 g}$ torus and orbifold models
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study the modular symmetry in magnetized $T^{2 g}$ torus and orbifold models. The $T^{2 g}$ torus has the modular symmetry $Γ_{g} = S p (2 g, Z)$ . The magnetic flux background breaks the modular symmetry to a certain normalizer $N_{g} (H)$ . We classify remaining modular symmetries by magnetic flux matrix types. Furthermore, we study the modular symmetry for wave functions on the magnetized $T^{2 g}$ and certain orbifolds. It is found that wave functions on magnetized $T^{2 g}$ as well as its orbifolds behave as the Siegel modular forms of weight $1 / 2$ and ${\tilde{N}}_{g} (H, h)$ , which is the metaplectic congruence subgroup of the double covering group of $N_{g} (H)$ , ${\tilde{N}}_{g} (H)$ . Then, wave functions transform nontrivially under the quotient group, ${\tilde{N}}_{g, h} = {\tilde{N}}_{g} (H) / {\tilde{N}}_{g} (H, h)$ , where the level $h$ is related to the determinant of the magnetic flux matrix. Accordingly, the corresponding four-dimensional chiral fields also transform nontrivially under ${\tilde{N}}_{g, h}$ modular flavor transformation with modular weight $- 1 / 2$ . We also study concrete modular flavor symmetries of wave functions on magnetized $T^{2 g}$ orbifolds.
Cited by 25
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Cited by 55
- 17 July 2023
- Published by Springer Nature in Journal of High Energy Physics
Quark mass hierarchies and CP violation in A4 × A4 × A4 modular symmetric flavor models
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study A₄× A₄× A₄ modular symmetric flavor models to realize quark mass hierarchies and mixing angles without fine-tuning. Mass matrices are written in terms of modular forms. At modular fixed points τ = i∞ and ω, A₄ is broken to Z₃ residual symmetry. When the modulus τ is deviated from the fixed points, modular forms show hierarchies depending on their residual charges. Thus, we obtain hierarchical structures in mass matrices. Since we begin with A₄× A₄× A₄, the residual symmetry is Z₃× Z₃× Z₃ which can generate sufficient hierarchies to realize quark mass ratios and absolute values of the CKM matrix |V_CKM| without fine-tuning. Furthermore, CP violation is studied. We present necessary conditions for CP violation caused by the value of τ. We also show possibilities to realize observed values of the Jarlskog invariant J_CP, quark mass ratios and CKM matrix |V_CKM| simultaneously, if (10) adjustments in coefficients of Yukawa couplings are allowed or moduli values are non-universal.
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- 17 July 2023
- Published by Springer Nature in Journal of High Energy Physics
Open Access
Quark mass hierarchies and CP violation in A4 × A4 × A4 modular symmetric flavor models
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study A₄× A₄× A₄ modular symmetric flavor models to realize quark mass hierarchies and mixing angles without fine-tuning. Mass matrices are written in terms of modular forms. At modular fixed points τ = i∞ and ω, A₄ is broken to Z₃ residual symmetry. When the modulus τ is deviated from the fixed points, modular forms show hierarchies depending on their residual charges. Thus, we obtain hierarchical structures in mass matrices. Since we begin with A₄× A₄× A₄, the residual symmetry is Z₃× Z₃× Z₃ which can generate sufficient hierarchies to realize quark mass ratios and absolute values of the CKM matrix |V_CKM| without fine-tuning. Furthermore, CP violation is studied. We present necessary conditions for CP violation caused by the value of τ. We also show possibilities to realize observed values of the Jarlskog invariant J_CP, quark mass ratios and CKM matrix |V_CKM| simultaneously, if (10) adjustments in coefficients of Yukawa couplings are allowed or moduli values are non-universal.
Cited by 55
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- 14 June 2023
- Published by arXiv in arXiv
Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study fermion zero-mode wavefunctions on $T^4/Z_N$ orbifold with background magnetic fluxes. The number of zero-modes is analyzed by use of $Sp(4,\mathbb{Z})$ modular transformation. Conditions needed to realize three generation models are clarified. We also study parity transformation in the compact space which leads to better understanding of relationship between positive and negative chirality wavefunctions.
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- 14 June 2023
- Published by arXiv in arXiv
Open Access
Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study fermion zero-mode wavefunctions on $T^4/Z_N$ orbifold with background magnetic fluxes. The number of zero-modes is analyzed by use of $Sp(4,\mathbb{Z})$ modular transformation. Conditions needed to realize three generation models are clarified. We also study parity transformation in the compact space which leads to better understanding of relationship between positive and negative chirality wavefunctions.
Open Access
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Cited by 13
- 5 June 2023
- Published by Springer Nature in Journal of High Energy Physics
Number of zero-modes on magnetized T4/ZN orbifolds analyzed by modular transformation
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study fermion zero-mode wavefunctions on T⁴/Z_N orbifold with background magnetic fluxes. The number of zero-modes is analyzed by use of Sp(4, ℤ) modular transformation. Conditions needed to realize three generation models are clarified. We also study parity transformation in the compact space which leads to better understanding of relationship between positive and negative chirality wavefunctions.
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- 5 June 2023
- Published by Springer Nature in Journal of High Energy Physics
Open Access
Number of zero-modes on magnetized T4/ZN orbifolds analyzed by modular transformation
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Shohei Takada, Hikaru Uchida
We study fermion zero-mode wavefunctions on T⁴/Z_N orbifold with background magnetic fluxes. The number of zero-modes is analyzed by use of Sp(4, ℤ) modular transformation. Conditions needed to realize three generation models are clarified. We also study parity transformation in the compact space which leads to better understanding of relationship between positive and negative chirality wavefunctions.
Cited by 13
Open Access
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- 4 June 2023
- Published by arXiv in arXiv
Three-generation solutions of equations of motion in heterotic supergravity
by Maki Takeuchi, Takanao Tsuyuki, Hikaru Uchida
We study the generation number of massless fermions in compactifications recently found in heterotic supergravity. The internal spaces are products of two-dimensional spaces of constant curvature, and the standard embedding is not assumed. The generation number is constrained by the equations of motion and the Bianchi identity. In the case that the Euler characteristics of the three internal submanifolds are $(2,-2,-2)$, the generation number is three or less. We also show that three-generation solutions exist for arbitrary Euler characteristics of the negatively curved 2-manifolds, and we present some explicit solutions.
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- 4 June 2023
- Published by arXiv in arXiv
Open Access
Three-generation solutions of equations of motion in heterotic supergravity
by Maki Takeuchi, Takanao Tsuyuki, Hikaru Uchida
We study the generation number of massless fermions in compactifications recently found in heterotic supergravity. The internal spaces are products of two-dimensional spaces of constant curvature, and the standard embedding is not assumed. The generation number is constrained by the equations of motion and the Bianchi identity. In the case that the Euler characteristics of the three internal submanifolds are $(2,-2,-2)$, the generation number is three or less. We also show that three-generation solutions exist for arbitrary Euler characteristics of the negatively curved 2-manifolds, and we present some explicit solutions.
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Cited by 20
- 26 April 2023
- Published by American Physical Society (APS) in Physical Review D
Index theorem on magnetized blow-up manifold of $T^{2} / Z_{N}$
by Tatsuo Kobayashi, Hajime Otsuka, Makoto Sakamoto, Maki Takeuchi, Yoshiyuki Tatsuta, Hikaru Uchida
We investigate blow-up manifolds of $T^{2} / Z_{N} (N = 2, 3, 4, 6)$ orbifolds with magnetic flux. First, we construct the blow-up manifolds and zero-mode wave functions on them more precisely. In particular, through an appropriate singular gauge transformation, winding numbers of wave functions on $T^{2} / Z_{N}$ can be replaced with localized curvature and localized flux at orbifold fixed points. In addition, since the blow-up manifolds have no singularities, we apply the Atiyah-Singer index theorem to them; the chiral zero-mode number is given by the total magnetic flux. It can be also applied for $T^{2} / Z_{N}$ orbifolds through the blow-up process, and then we find that it is consistent with the zero-mode counting formula in M. Sakamoto et al. [Zero-mode counting formula and zeros in orbifold compactifications, Phys. Rev. D 102, 025008 (2020).]. Furthermore, the Atiyah-Singer index theorem shows that an additional degree of freedom of localized flux gives new chiral zero modes. We study their wave functions and then we find that they correspond to localized modes at the orbifold singular points. We also calculate their Yukawa couplings.
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- 26 April 2023
- Published by American Physical Society (APS) in Physical Review D
Open Access
Index theorem on magnetized blow-up manifold of $T^{2} / Z_{N}$
by Tatsuo Kobayashi, Hajime Otsuka, Makoto Sakamoto, Maki Takeuchi, Yoshiyuki Tatsuta, Hikaru Uchida
We investigate blow-up manifolds of $T^{2} / Z_{N} (N = 2, 3, 4, 6)$ orbifolds with magnetic flux. First, we construct the blow-up manifolds and zero-mode wave functions on them more precisely. In particular, through an appropriate singular gauge transformation, winding numbers of wave functions on $T^{2} / Z_{N}$ can be replaced with localized curvature and localized flux at orbifold fixed points. In addition, since the blow-up manifolds have no singularities, we apply the Atiyah-Singer index theorem to them; the chiral zero-mode number is given by the total magnetic flux. It can be also applied for $T^{2} / Z_{N}$ orbifolds through the blow-up process, and then we find that it is consistent with the zero-mode counting formula in M. Sakamoto et al. [Zero-mode counting formula and zeros in orbifold compactifications, Phys. Rev. D 102, 025008 (2020).]. Furthermore, the Atiyah-Singer index theorem shows that an additional degree of freedom of localized flux gives new chiral zero modes. We study their wave functions and then we find that they correspond to localized modes at the orbifold singular points. We also calculate their Yukawa couplings.
Cited by 20
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Cited by 18
- 3 April 2023
- Published by Springer Nature in Journal of High Energy Physics
Remark on modular weights in low-energy effective field theory from type II string theory
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Hajime Otsuka, Shohei Takada, Hikaru Uchida
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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- 3 April 2023
- Published by Springer Nature in Journal of High Energy Physics
Open Access
Remark on modular weights in low-energy effective field theory from type II string theory
by Shota Kikuchi, Tatsuo Kobayashi, Kaito Nasu, Hajime Otsuka, Shohei Takada, Hikaru Uchida
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.
Cited by 18

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