Number of zero-modes on magnetized T4/ZN orbifolds analyzed by modular transformation

Kikuchi, Shota; Kobayashi, Tatsuo; Nasu, Kaito; Takada, Shiro; Uchida, Hitoshi

doi:10.1007/jhep06(2023)013

J. High Energ. Phys.

2023

DOI: 10.1007/jhep06(2023)013

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Number of zero-modes on magnetized T4/ZN orbifolds analyzed by modular transformation

Shota Kikuchi

Tatsuo Kobayashi

Kaito Nasu

et al.

Abstract: We study fermion zero-mode wavefunctions on T4/ZN 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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Cited by 5 publications

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Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Kikuchi,

Kobayashi,

Nasu

et al. 2024

J. High Energ. Phys.

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We study an approach to construct Siegel modular forms from Sp(6, Z). Zero-mode wave functions on T6 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 TI, TII and TIII as well as the S-symmetry remain. Consequently, we obtain Siegel modular forms with three moduli parameters (ω1, ω2, ω3), 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, ω1 = i∞, the Siegel modular forms have hierarchical values depending on their TI-charges. We show the deviation of ω1 from the cusp can generate large quark mass hierarchies without fine-tuning. Furthermore CP violation is induced by deviation of ω2 from imaginary axis.

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Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Kikuchi,

Kobayashi,

Nasu

et al. 2024

J. High Energ. Phys.

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Trace Conservation Laws in T2/Zm Orbifold Gauge Theories

Takeuchi,

Inagaki

2024

Progress of Theoretical and Experimental Physics

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Gauge theory compactified on an orbifold is defined by gauge symmetry, matter contents, and boundary conditions. There are equivalence classes (ECs), each of which consists of physically equivalent boundary conditions. We propose the powerful necessary conditions, trace conservation laws (TCLs), which achieve a sufficient classification of ECs in U(N) and SU(N) gauge theories on T2/Zm orbifolds (m = 2, 3, 4, 6). The TCLs yield the equivalent relations between the diagonal boundary conditions without relying on an explicit form of gauge transformations. The TCLs also show the existence of off-diagonal ECs, which consist only of off-diagonal matrices, on T2/Z4 and T2/Z6. After the sufficient classification, the exact numbers of ECs are obtained.

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Zero-modes in magnetized T6/ZN orbifold models through Sp(6,
Kikuchi,
Kobayashi,
Nasu
et al. 2023
Phys. Rev. D

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Number of zero-modes on magnetized T4/ZN orbifolds analyzed by modular transformation

Cited by 5 publications

References 35 publications

Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Trace Conservation Laws in T2/Zm Orbifold Gauge Theories

Zero-modes in magnetized T6/ZN orbifold models through Sp(6,
Kikuchi,
Kobayashi,
Nasu
et al. 2023
Phys. Rev. D

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Number of zero-modes on magnetized T4/ZN orbifolds analyzed by modular transformation

Cited by 5 publications

References 35 publications

Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Sp(6, Z) modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $$\widetilde{\Delta }\left(96\right)$$

Trace Conservation Laws in T2/Zm Orbifold Gauge Theories

Zero-modes in magnetized T6/ZN orbifold models through Sp(6,Kikuchi, Kobayashi, Nasu et al. 2023Phys. Rev. D

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Zero-modes in magnetized T6/ZN orbifold models through Sp(6,
Kikuchi,
Kobayashi,
Nasu
et al. 2023
Phys. Rev. D