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PreprintCC BY 4.0arXiv

Eclectic flavour symmetries without flavons

  • Ferruccio Feruglio
  • Antonio Marrone
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Abstract

We develop a new framework in which eclectic groups are realised as flavour symmetries without flavons. Focusing on the group Ω(1), we show that it can be realised as a finite image of the integral Jacobi group, i.e. the semidirect product of H(ℤ) with SL(2,ℤ), acting on two moduli (τ,z). The Heisenberg subgroup H(ℤ) leaves the modulus τ unchanged, and its finite image Δ(27) plays the role of the traditional flavour symmetry. We provide the ingredients needed to construct supersymmetric Jacobi-invariant theories, both in globally supersymmetric theories and in supergravity. We develop a realistic model of fermion masses within this framework and formulate a consistent CP symmetry, which can be imposed at the Lagrangian level and broken spontaneously by the moduli. We discuss how the conventional eclectic-flavour description is recovered in an appropriate limit. We also extend this geometric interpretation to the T2/ℤ4 and T2/ℤ2 eclectic building blocks, and clarify why the T2/ℤ6 case is structurally different.

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Cite

BibTeXRIS
BibTeX
@misc{feruglio2026eclectic,
  title = {{Eclectic flavour symmetries without flavons}},
  author = {Ferruccio Feruglio and Antonio Marrone},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16118},
  eprint = {2609.16118},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16118},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Eclectic flavour symmetries without flavons
AU  - Ferruccio Feruglio
AU  - Antonio Marrone
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16118
UR  - https://arxiv.org/abs/2609.16118
AB  - We develop a new framework in which eclectic groups are realised as flavour symmetries without flavons. Focusing on the group Ω(1), we show that it can be realised as a finite image of the integral Jacobi group, i.e. the semidirect product of H(ℤ) with SL(2,ℤ), acting on two moduli (τ,z). The Heisenberg subgroup H(ℤ) leaves the modulus τ unchanged, and its finite image Δ(27) plays the role of the traditional flavour symmetry. We provide the ingredients needed to construct supersymmetric Jacobi-invariant theories, both in globally supersymmetric theories and in supergravity. We develop a realistic model of fermion masses within this framework and formulate a consistent CP symmetry, which can be imposed at the Lagrangian level and broken spontaneously by the moduli. We discuss how the conventional eclectic-flavour description is recovered in an appropriate limit. We also extend this geometric interpretation to the T^2/ℤ_4 and T^2/ℤ_2 eclectic building blocks, and clarify why the T^2/ℤ_6 case is structurally different.
ER  -