Download - grand gauge-Higgs unification
![Page 1: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/1.jpg)
based on : based on : arXiv:1103.1234arXiv:1103.1234 (appeared today) (appeared today)in collaboration with :in collaboration with : K. Kojima (Kyushu) & K. Takenaga (Kumamoto Health Science) K. Kojima (Kyushu) & K. Takenaga (Kumamoto Health Science)
grand gauge-Higgs unification
山下 敏史( 名古屋 益川塾 )
2011/3/8 2011/3/8 @@ 素粒子物理学の進展2011
![Page 2: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/2.jpg)
Introduction
Gauge-Higgs Unification
5D theory
with KK modes gauge field
Higgs
compactification
4D theory
gauge field
scalar field
D.B. Fairlie (1979)N.S. Manton (1979)
Y.Hosotani (1989-)
Hosotani mechanism
![Page 3: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/3.jpg)
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)
in models w/ no chiral fermions
Y. Kawamura (2000-)
• after : mainly applied to EW breaking
• chiral fermion• fundamental repr.
Hosotani’s talk
GUT breaking in models w/ chiral fermion?K.Kojima & K.Takenaga & T.Y.
![Page 4: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/4.jpg)
Introduction
difficulty• orbifold action projects out adjoint scalars
K.Kojima & K.Takenaga & T.Y.
• this difficulty is shared w/ heterotic string
- well studied, classified w/ Kac-Moody level- ``diagonal embedding” method
Kuwakino’s talk
Why can’t we use this in our pheno. models?
![Page 5: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/5.jpg)
Plan• IntroductionIntroduction• massless adjoint scalarmassless adjoint scalar• FermionsFermions• ApplicationsApplications• SummarySummary
![Page 6: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/6.jpg)
ex)
massless adjoint scalar
Orbifold
Fields may not be invariant!
ex)
symm. transformation
![Page 7: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/7.jpg)
ex) SU(3) SU(2)*U(1)
massless adjoint scalar
Orbifold breaking Y.Kawamura (2000)
projected out
![Page 8: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/8.jpg)
massless adjoint scalar
diagonal embedding K.R.Dienes & J.March-Russel (1996)
diagonal part permutation as orbifold action
eigenvalues:
zero-modes:
adjoint scalar
ex)
![Page 9: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/9.jpg)
Plan• IntroductionIntroduction• massless adjoint scalarmassless adjoint scalar• FermionsFermions• ApplicationsApplications• SummarySummary
![Page 10: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/10.jpg)
Fermions
exchange symmetry
: vector-like
K.Kojima & K.Takenaga & T.Y.
2 partner
when R1=R2
: chiral
• when R1=R2 (=R) : ex) SU(5) w/ R=5
![Page 11: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/11.jpg)
Fermions
KK spectrum
K.Kojima & K.Takenaga & T.Y.
BG:
(basically) same as S1
• when R2 is trivial : completely same
![Page 12: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/12.jpg)
Fermions
KK spectrum
K.Kojima & K.Takenaga & T.Y.
BG:
(basically) same as S1
• when R2 is non-trivial : slightly different
as if non-local interaction
![Page 13: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/13.jpg)
Fermions
KK spectrum
K.Kojima & K.Takenaga & T.Y.
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.
![Page 14: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/14.jpg)
Plan• IntroductionIntroduction• massless adjoint scalarmassless adjoint scalar• FermionsFermions• ApplicationsApplications• SummarySummary
![Page 15: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/15.jpg)
Applications K.Kojima & K.Takenaga & T.Y.
• it is not easy to realize vacua where SU(5) is broken down to SM, as global minima.
The results in literatures can be easily reproduced, besides chiral fermions (on the branes).
SU(5)
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
![Page 16: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/16.jpg)
Summary
• We propose a novel way to break GUT-symm. via the Hosotani mechanism.
• chiral fermions on branes• adjoint scalars by diagonal embedding
• It turns out KK spectra are basically the same as in S1 models
results in literatures are easily reproduced.
• model w/ desired vacuum as local minimum.• SU(5) GSM is not easy as global minima
![Page 17: grand gauge-Higgs unification](https://reader035.vdocuments.net/reader035/viewer/2022062309/56813b76550346895da48590/html5/thumbnails/17.jpg)
Summary
• SUSY and/or RS• doublet-triplet splitting• gauge coupling unification• concrete model building …
future works