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: (appeared today)
in collaboration with :
K. Kojima (Kyushu) & K. Takenaga (Kumamoto Health Science)

2. 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-)

3. 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.

4. 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?

5. Plan Introduction massless adjoint scalar Fermions Applications
Summary

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

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

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

9. Plan Introduction massless adjoint scalar Fermions Applications
Summary

10. 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

11. 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

12. 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

13. 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.

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 …