Quark masses from Gaugino Condensation in String Theories

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Quark masses from Gaugino Condensation in String
Theories

• Christos Kokorelis

Talk at Corfu Summer Institute,
Theory-Cosmology-Phenomenology, September 8,
2009
Based on C.K, 0812.4804hep-th C.K,
V.E.Mayes, D,V. Nanopoulos, 0907.4028  hep-th
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Basic Idea

• Generate masses for all generations, reproduce
  hierarchical QL masses
• Examples Toroidal orientifolds IIA/IIB
• 1 family get a mass, 2 massless ones
  factorization of Yukawas Non-zero Iab in 2
  different tori Cremades, Ibanez, Marchesano
• Additional Higgs evade the problem for
  specific values
• of the moduli Cvetic, Langacker, Shiu, Chen,
  Li, Mayes, Nanopoulos in Pati-Salam GUTS
• SU(4)c x SU(2)L x SU(2)R like D-brane string
  models

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Basic Idea continued

• However, e.g. in SU(5)/flipped SU(5) GUTS
  missing up-quark masses do not get generated
  perturbatively!
• Possible Non-perturbative solutions
• D-brane Instantons
• Blumenhagen, Cvetic, Lust, Richter,
  Weigand
• Perturbative Solution Gaugino Condensates
• C.K, Mayes, Nanopoulos

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OutLine

• Part I Missing mass terms for SU(5) GUTS
• Part II Perturbative solution to missing quark
  masses in SU(5), flipped SU(5) orientifolds
• Part III Instanton solutions inspired from the
  perturbative solution
• OutLook

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• PART I
• Missing mass terms for SU(5)
• Orientifold GUTS

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Missing mass terms for u-quarks in orientifolds

• SU(5)/FSU(5) GUTS in (IIA, IIB)/OR orientifolds
  are missing up/down quark masses 10 10 5
  coupling does not exist from U(1) charge
  conservation

• A typical SU(5)/FSU(5) U/D quark mass term

10 (2, 0) 10 (2, 0) 5 H (1, 1)
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A typical SU(5) GUT

Bachas, Blumenhagen, Kors, Lust, Ott, Ellis,
Kanti, Nanopoulos, Axenides, C.K, Floratos,
Bianchi, Weigand
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Historical facts
SU(5) GUT
Flipped SU(5) GUT
Yukawa mass terms SU(5) 10 10 5H eijklm 10i
10j 5Hm u c3 u3 lth0gt Yukawa mass terms
FSU(5) 10 10 5H eijklm 10i 10j 5Hm dc3 d3
lth0gt
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Part II Perturbative solution to missing
quark masses in SU(5), flipped SU(5) orientifolds

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The coupling
exists from charge and gauge invariance
gets charged SU(5) x U(1)
The
or SU(5) x Sp(2) x..
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The
condenses

• In the case of chiral symmetry breaking as SU(3)
  symmetry is not spontaneously broken we take the
  vacuum to be SU(3) symmetric
• lt0QL UR0gt µ3 (1,2)-1/2

Ibanez, Marchesano,Rabadan
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SU(5)/FSU(5)

• In our case, the condensate (1,2)
• and provides masses to U/D quarks
• When it is charged under SU(5) x Sp(2)
• Or (FSU(5) x Sp(2))

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Sp(2) strongly coupled
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blt0 ,
0
1016 lt Ms lt 1018
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Conclussions/Outlook
We have presented evidence for the existence of
condensates able to give masses to the missing
up/down quark masses in SU(5)/FSU(5) GUTS in
toroidal orientifolds The mechanism may be
applied to F-theory constructions