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Novel Approach to Gauge-Higgs Unification: Hosotani Mechanism and Adjoint Scalars

Explore the revolutionary Hosotani mechanism for Gauge-Higgs unification in particle physics, employing diagonal embedding and chiral fermions on branes. Discover how KK spectra mirror those of S1 models, while challenges in realizing SU(5) breaking to GSM persist. Future work entails investigating SUSY, RS, doublet-triplet splitting, gauge coupling unification, and concrete model building. This work presents a fresh perspective on GUT symmetry breaking and fermionic interactions in a cutting-edge theoretical framework.

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Novel Approach to Gauge-Higgs Unification: Hosotani Mechanism and Adjoint Scalars

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  1. grand gauge-Higgs unification 山下　敏史 (名古屋  益川塾) 2011/3/8 @素粒子物理学の進展２０１１ based on : arXiv:1103.1234 (appeared today) in collaboration with : K. Kojima (Kyushu) & K. Takenaga (Kumamoto Health Science)

  2. Introduction D.B. Fairlie(1979) N.S. Manton(1979) • Gauge-Higgs Unification 5D theory gauge field compactification 4D theory gauge field scalar field with KK modes Higgs Hosotani mechanism Y.Hosotani (1989-)

  3. Introduction • Hosotani mechanism Y. Hosotani(1989-) • symmetry breaking by VEVs of Wilson line phase zero-mode of A5 • beforeorbifold breaking : applied to GUT breaking (A5 : adjoint) Y. Kawamura (2000-) in models w/ no chiral fermions chiral fermion fundamental repr. • after: mainly applied to EW breaking Hosotani’s talk GUT breaking in models w/ chiral fermion? K.Kojima & K.Takenaga & T.Y.

  4. Introduction • difficulty K.Kojima & K.Takenaga & T.Y. orbifold action projects out adjoint scalars this difficulty is shared w/ heterotic string Kuwakino’s talk • well studied, classified w/ Kac-Moody level • ``diagonal embedding” method Why can’t we use this in our pheno. models?

  5. Plan • Introduction • massless adjoint scalar • Fermions • Applications • Summary

  6. massless adjoint scalar • Orbifold ex) Fields may notbe invariant! ex) symm. transformation

  7. massless adjoint scalar • Orbifold breaking Y.Kawamura (2000) ex) SU(3) SU(2)*U(1) projected out

  8. eigenvalues: ex) zero-modes: massless adjoint scalar • diagonal embedding K.R.Dienes & J.March-Russel (1996) diagonal part permutation as orbifold action adjoint scalar

  9. Plan • Introduction • massless adjoint scalar • Fermions • Applications • Summary

  10. Z2 partner when R1=R2 when R1=R2 (=R) : ex) SU(5) w/R=5 Fermions K.Kojima & K.Takenaga & T.Y. • exchange symmetry : vector-like : chiral

  11. Fermions K.Kojima & K.Takenaga & T.Y. • KK spectrum (basically) same as S1 BG: when R2 is trivial : completely same

  12. Fermions K.Kojima & K.Takenaga & T.Y. • KK spectrum (basically) same as S1 BG: when R2 is non-trivial : slightly different as if non-local interaction

  13. the same as R1*R2 fermion in S1, while it behaves as R1*R2 under Gdiag. Fermions K.Kojima & K.Takenaga & T.Y. • KK spectrum (basically) same as S1 BG: when R2 is non-trivial : slightly different

  14. Plan • Introduction • massless adjoint scalar • Fermions • Applications • Summary

  15. Applications K.Kojima & K.Takenaga & T.Y. The results in literatures can be easily reproduced, besides chiral fermions (on the branes). • SU(5) • it is not easy to realize vacua where SU(5) is broken down to SM, as global minima. A.T.Davies & A.McLachlan (1989) • it is claimed the desired minimum can be realized w/ fermions : 5, 10 scalars : 5, 3*15, as a local minimum V.B.Svetovoi & N.G.Khariton,(1986) anti-periodic fermion

  16. Summary • We propose a novel way to break GUT-symm. via the Hosotani mechanism. adjoint scalars by diagonal embedding chiral fermions on branes • It turns out KK spectra are basically the same as in S1 models results in literatures are easily reproduced. SU(5) GSM is not easy as global minima model w/ desired vacuum as local minimum.

  17. Summary • future works • SUSY and/or RS • doublet-triplet splitting • gauge coupling unification • concrete model building …

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