grand gauge-Higgs unification

1
grand gauge-Higgs unification

• ?? ??
• (??? ? ???)

2011/3/8 _at_?????????2011
based on arXiv1103.1234 (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

• 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

Hosotanis 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

Kuwakinos talk

• well studied, classified w/ Kac-Moody level
• diagonal embedding method

Why cant we use this in our pheno. models?
5
Plan

• Introduction
• massless adjoint scalar
• Fermions
• Applications
• Summary

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massless adjoint scalar

• Orbifold

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

• Orbifold breaking

Y.Kawamura (2000)
ex) SU(3) ? SU(2)U(1)
projected out
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massless adjoint scalar

• diagonal embedding

K.R.Dienes J.March-Russel (1996)
diagonal part
permutation as orbifold action
adjoint scalar
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Plan

• Introduction
• massless adjoint scalar
• Fermions
• Applications
• Summary

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Fermions
K.Kojima K.Takenaga T.Y.

• exchange symmetry

vector-like
chiral
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Fermions
K.Kojima K.Takenaga T.Y.

• KK spectrum

(basically) same as S1
BG

• when R2 is trivial completely same

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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
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Fermions
K.Kojima K.Takenaga T.Y.

• KK spectrum

(basically) same as S1
BG

• when R2 is non-trivial slightly different

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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, 315, as a local
  minimum

V.B.Svetovoi N.G.Khariton,(1986)
anti-periodic fermion
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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