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 Gauge-Higgs Unification 5D theory gauge field 4D theory 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-)

Introduction Hosotani mechanism symmetry breaking by VEVs of Y. Hosotani　 (1989-) symmetry breaking by VEVs of Wilson line phase zero-mode of A5 before orbifold 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.

Introduction difficulty orbifold action projects out adjoint scalars 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?

Plan Introduction massless adjoint scalar Fermions Applications Summary

massless adjoint scalar Orbifold ex) Fields may not be invariant! ex) symm. transformation

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

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

Plan Introduction massless adjoint scalar Fermions Applications Summary

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

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

as if non-local interaction 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

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

Plan Introduction massless adjoint scalar Fermions Applications Summary

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

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.

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