Three%20family%20models%20from%20the%20Heterotic%20string

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Three family models from the Heterotic string
Stuart Raby
w/ R.J. Zhang and T. Kobayashi, Phys.
Lett. B593, 262 (2004) Nucl. Phys.
B704, 3 (2005)
String Phenomenology 2005 Munich,
Germany
June 13, 2005
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Phenomenological Guidelines

1. Preserve gauge coupling unification
2. Low energy SUSY MZ ltlt MG
3. Quarks and leptons in 16 of SO(10)
4. Higgs in 10
5. Preserve GUT relations for 3rd family Yukawa
6. Natural See-Saw scale MG
7. Use intuition from Orbifold GUTs

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E8 x E8 Heterotic string in 10D
Compactify 6D on (T2)3
Then mod by Z6 (Z3 x Z2) and Add Wilson
lines
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First consider (T2)3/Z3 W3
Wilson line in
SU3 torus
Massless modes From Untwisted sector
(G2 , SU3) twisted sector
E6 GUT in 5D
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Then add Z2 orbifold W2
in long direction
P
P
( V2 )
( V2 W2 )
E6
SO(10)
SU(4)xSU(2)LxSU(2)R
F3 (4,2,1), F3c (4c,1,2) , H (1,2,2)
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E6 Orbifold GUT on M4 x S1/(Z2xZ2)
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Exotics
Two families sit on Z2 fixed points !!
D4 family symmetry !!
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D4 family symmetry

singlet
doublet
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Z2 twisted sector
Extra color triplets !!
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To summarize

• 3rd family in bulk

gauge-Yukawa unification

• 1st and 2nd families on Z2 fixed points

D4 family symmetry

Higgs for PS symmetry breaking
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PS symmetry breaking
F and D flat direction breaks PS to SM gives
mass to all SM non-singlets
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Gauge coupling unification ?
4D GUT

5D Orbifold GUT
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Gauge coupling unification
and -- modes are in overlap of

and
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B.C.s
Weak

Strong
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Successes

• Gauge coupling unification

• 3rd generation and Higgs in bulk
• -gt gauge-Yukawa unif.

• D4 family symmetry family hierarchy
• suppress flavor violation

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D4 family symmetry

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So whats the problem ?

• Exotics !

• Extra color triplets !

• NO R parity !!!

Solution ZN x Z2 orbifolds ??
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Few Exotics

Fractional electric charge BUT Vector-like
!!
Mass at String scale
Technical difficulty
Not all exotics get mass
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R parity ??

R parity !!
Technical difficulty
T4 ( U3 T2 T1 T1 )
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R parity ??

R parity !!
Technical difficulty
T4 ( U3 T2 )
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Conclusions

• New 3 family E6 orbifold GUT
• 3rd generation -- gauge-Yukawa unif.
• D4 family symmetry family hierarchy
• suppress flavor violation
• Few vector-like exotics
• Extra color triplets
• NO R parity

Possible solution in ZNxZ2 orbifold