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

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

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.

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?

Plan• IntroductionIntroduction• massless adjoint scalarmassless adjoint scalar• FermionsFermions• ApplicationsApplications• SummarySummary

ex)

massless adjoint scalar

Orbifold

Fields may not be invariant!

ex)

symm. transformation

ex) SU(3) SU(2)*U(1)

massless adjoint scalar

Orbifold breaking Y.Kawamura (2000)

projected out

massless adjoint scalar

diagonal embedding K.R.Dienes & J.March-Russel (1996)

diagonal part permutation as orbifold action

eigenvalues:

zero-modes:

adjoint scalar

ex)

Plan• IntroductionIntroduction• massless adjoint scalarmassless adjoint scalar• FermionsFermions• ApplicationsApplications• SummarySummary

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

Fermions

KK spectrum

K.Kojima & K.Takenaga & T.Y.

BG:

(basically) same as S1

• when R2 is trivial : completely same

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

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.

Plan• IntroductionIntroduction• massless adjoint scalarmassless adjoint scalar• FermionsFermions• ApplicationsApplications• SummarySummary

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

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

Summary

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

future works