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PreprintCC BY 4.0arXiv

Note on arithmetic structure of modulus vacua in flux compactifications

  • Yukiya Furuta
  • Tatsuo Kobayashi
  • Tomoyasu Kori
  • Shuhei Miyamoto
  • Ryusei Nishida
  • Hajime Otsuka
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Abstract

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') 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
@misc{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},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.24054},
  eprint = {2608.24054},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.24054},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
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  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.24054
UR  - https://arxiv.org/abs/2608.24054
AB  - 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') 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.
ER  -