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Peer-reviewedCC BY 4.0Journal of High Energy Physics

Note on arithmetic structure of modulus vacua in flux compactifications

  • Yukiya Furuta1
  • Tatsuo Kobayashi1
  • Tomoyasu Kori1
  • Shuhei Miyamoto1
  • Ryusei Nishida1
  • Hajime Otsuka2
  1. 1Hokkaido University
  2. 2Kyushu University
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Abstract

A bstract : We study modulus stabilization by background fluxes. Within the truncated complex-structure sector, the F-term conditions of the complex structure moduli are described by a holomorphic quadratic equation. As concrete examples, we consider the T6/(ℤ2× ℤ2′) T 6 / ℤ 2 × ℤ 2 ′ orientifold model and a simple Calabi-Yau compactification. The modulus values show specific patterns. For example, they exhibit a structure related to the Farey sequence. The void structure appears around modulus vacua with high degeneracies. We find a correlation between the degeneracy and the void area. The modulus vacua are related by discrete Abelian symmetries generated by the Gauss composition law, which includes the CP symmetry. Spontaneous CP violation is also discussed.

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Cite

BibTeXRIS
BibTeX
@article{furuta2026note,
  title = {{Note on arithmetic structure of modulus vacua in flux compactifications}},
  author = {Yukiya Furuta and Tatsuo Kobayashi and Tomoyasu Kori and Shuhei Miyamoto and Ryusei Nishida and Hajime Otsuka},
  journal = {Journal of High Energy Physics},
  year = {2026},
  month = oct,
  doi = {10.1007/jhep10(2026)160},
  url = {https://link.springer.com/article/10.1007/JHEP10(2026)160},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Note on arithmetic structure of modulus vacua in flux compactifications
AU  - Yukiya Furuta
AU  - Tatsuo Kobayashi
AU  - Tomoyasu Kori
AU  - Shuhei Miyamoto
AU  - Ryusei Nishida
AU  - Hajime Otsuka
PY  - 2026
DA  - 2026/10/14
JO  - Journal of High Energy Physics
DO  - 10.1007/jhep10(2026)160
UR  - https://link.springer.com/article/10.1007/JHEP10(2026)160
AB  - A bstract : We study modulus stabilization by background fluxes. Within the truncated complex-structure sector, the F-term conditions of the complex structure moduli are described by a holomorphic quadratic equation. As concrete examples, we consider the T^6/(ℤ_2× ℤ_2^′) T 6 / ℤ 2 × ℤ 2 ′ orientifold model and a simple Calabi-Yau compactification. The modulus values show specific patterns. For example, they exhibit a structure related to the Farey sequence. The void structure appears around modulus vacua with high degeneracies. We find a correlation between the degeneracy and the void area. The modulus vacua are related by discrete Abelian symmetries generated by the Gauss composition law, which includes the CP symmetry. Spontaneous CP violation is also discussed.
SN  - 1029-8479
ER  -