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Constructing 5D Orbifold GUTs from Heterotic Strings. Stuart Raby. w/ R.J. Zhang and T. Kobayashi Phys. Lett. B593, 262 (2004) & Nucl. Phys. B704, 3 (2005) w/ A. Wingerter and P. Vaudrevange, in progress. Fermilab Theory Seminar. - PowerPoint PPT Presentation
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Constructing 5D Orbifold GUTs from Heterotic Strings
w/ R.J. Zhang and T. Kobayashi Phys. Lett. B593, 262 (2004) & Nucl. Phys. B704, 3 (2005) w/ A. Wingerter and P. Vaudrevange, in progressFermilab Theory Seminar
Stuart Raby
May 25, 2006
In 2007, the LHC turns on; hopefully opening up a new age of discovery. String theory is by far the best candidate for a self-consistent quantum theory of gravity. Moreover, it provides a framework for a true theory of everything.
Estimates suggest there are more than 10300 string vacua. The string vacuum fixes the gauge group, the number of families, fermion masses and supersymmetry breaking. Many have searched for
phenomenologically acceptable string vacua.
Yet we do not know whether even one string vacuum exists which looks like the real world.
This talk describes a new search in an old direction -- the weakly coupled heterotic string.
Our results are promising; already providing some interesting new models. We are guided in our approach by recent progress in understanding model
building in 5 and 6 dimensional orbifold SUSY GUT field theories.
Phenomenological Guidelines
1. Preserve gauge coupling unification2. Low energy SUSY MZ << MG3. Quarks and leptons in 16 of SO(10)4. Higgs in 105. Preserve GUT relations for 3rd family Yukawa6. “Natural” See-Saw scale ~ MG
7. Use intuition from Orbifold GUTs
Outline
3 Family Orbifold GUT on M4 x S1/(Z2xZ2’)
Heterotic string compactified on [T2]3/Z6
+ Wilson lines
Consider E6 example
Title of talk 5
Title of talk 6
Title of talk 7
E6 Orbifold GUT on M4 x S1/(Z2xZ2’)
E8 x E8 Heterotic string in 10DCompactify 6D on
(T2)3
Then mod by Z6 = (Z3 x Z2) and Add Wilson linesZ6 embedded in E8 x E8 gauge lattice
as shift V6 : consistent with mod. inv. !
First consider (T2)3/Z3 + W3 [Wilson line in SU3 torus]
Massless modesFrom Untwisted sector + (G2 , SU3) twisted sector
E6 GUT in 5D
Then add Z2 orbifold + W2 [in long direction]
E6 SO(10) SU(4)xSU(2)LxSU(2)R
F3 = (4,2,1), F3c = (4c,1,2) , H = (1,2,2)
P P’ ( V2 ) ( V2+ W2 )
Two families sit on Z2 fixed points !!
D4 family symmetry !!
Exotics
D4 family symmetry 4 1 3 2
1 1 2 3 2 2
1, , ,
0 1 1 0: :
1 0 0 1
D i
f f f f
1
2
ff
doublet 3f singlet
Extra color triplets !!
Z2 twisted sector
E6 Orbifold GUT on M4 x S1/(Z2xZ2’)
3rd family in bulk gauge-Yukawa unification
1st and 2nd families on Z2 fixed pointsD4 family symmetry
Higgs for PS symmetry breaking
53 3
0
27 27R
cg dy gHF FR
To summarize
PS symmetry breaking
1 4 4 1 1 1 1 2 2c c c c c cW SCC C S
F and D flat direction breaksPS to SM + gives mass to all SM non-singlets
Gauge coupling unification ?
3
2 2log 6MSSM G
i ii G
Mb
4D GUT
5D Orbifold GUT
6
2 2 log log
1 log 12
stringMSSM PSPSi brane i
i string PS
string stringEPS PS
ic c
MMb b bM
M Mb b b
M M
Gauge coupling unification
++ and -- modes are in overlap of
10SO6 2RSU SUand
2 3
PS PSb b 2 3
PS PSb b
2 3brane braneb b3 152 7 10PS GM e M GeV 1 1
2 3
22
4Planck
s s
MM
2 17 12 10 450s G sM Max e M GeV
Weak
2
53
2 1
2 4Pl
s
MMM
3 152
1
2
7 10
s G
c PS G
G
M M M
M M e M GeV
M
B.C.s
Strong
Successes
3rd generation and Higgs in bulk -> gauge-Yukawa unif.
D4 family symmetry : family hierarchy + suppress flavor violation
Gauge coupling unification 23
330
0.0153 10latticep eGeV yrs
335.4 10 . [ ]yrs S K
D4 family symmetry
So what’s the problem ? Exotics
So what now ? Search for R parity inv. theory Z3 x Z2 or Alternate orbifold construct
NO R parity !!
BUT Vector-like
May be OK ?
OK ! IF massive
New Search Z2 x Z4 orbifold
V2 x V4 120 inequivalent possibilities
W1 and/or W2 500,000 possible models
Narrow the searchConsider eg. MSSM in 4D Why bother with GUTs Demand - 3 ( 3, 2 ) + 6 ( 3* , 1 ) + > 5 ( 1 , 2 ) TYPICALLY have Chiral Exotics i.e. Wrong Hypercharge
w/ Wingerter & Vaudrevange
Solution - Demand PS or SU(5) intermediate sym. & identify hypercharge ½ ( B – L) + T3R in PS or Y in SU(5)
I. MSSM in 4D w/ 3 families & NO chiral
exotics Find PS -> SM - 6
models SU(5) -> SM - 40
modelsII. Pati – Salam in 4D w/ 3 families, PS Higgs & NO chiral exotics Find ~ 220 models
Title of talk 26
Z2 x Z4 orbifold constructionOne example : preliminary
Part of third family in bulk => heavy top
Two light families on (0,1) fixed poiints
Spectrum
2/3 -2/3
u d
11 1/3 1/3
3 Q Q Q
3 u e d 7 d d
3 L 7 H H
8 E E 8 q q ...
Order S0 : top mass S2 : bottom + tau mass term
Conclusions
New 3 family E6 orbifold GUT 3rd generation -- gauge-Yukawa unif. D4 family symmetry : family hierarchy + suppress flavor violation Few vector-like exotics NO R parity
Z2 x Z4 & Z2 x Z3 search in progress
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