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grand gauge-Higgs unification

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). Introduction. D.B. Fairlie (1979) N.S. Manton (1979).

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grand gauge-Higgs unification

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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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