Sliding Singlet Mechanism and E6 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
Gauge-Higgs Unification
5D theory
D.B. Fairlie (1979)
N.S. Manton (1979)
gauge field
compactification
4D theory
with KK modes
gauge field
scalar field
Higgs
Hosotani
mechanism
Y.Hosotani (1989-)
Introduction
Hosotani mechanism
Y. Hosotani (1989-)
• symmetry breaking by VEVs of
Wilson line phase zero-mode of A5
• before orbifold breaking :
Y. Kawamura (2000-)
applied to GUT breaking (A5 : adjoint)
in models w/ no chiral fermions • chiral fermion
• fundamental repr.
• after :
Hosotani’s talk
mainly applied to EW breaking
GUT breaking in models w/ chiral fermion?
K.Kojima & K.Takenaga & T.Y.
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?
Plan
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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
diagonal part
K.R.Dienes & J.March-Russel (1996)
permutation
eigenvalues:
as orbifold action
ex)
adjoint scalar
zero-modes:
Plan
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Introduction
massless adjoint scalar
Fermions
Applications
Summary
Fermions
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
K.Kojima & K.Takenaga & T.Y.
KK spectrum
BG:
• when R2 is trivial : completely same
(basically)
same as S1
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
K.Kojima & K.Takenaga & T.Y.
KK spectrum
BG:
(basically)
same as S1
• when R2 is non-trivial : slightly different
the same as R1*R2 fermion in S1,
while it behaves as R1*R2 under Gdiag.
Plan
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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
anti-periodic fermion
V.B.Svetovoi & N.G.Khariton,(1986)
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
…

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