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Quark masses from Gaugino Condensation in String Theories. Talk at Corfu Summer Institute, Theory-Cosmology-Phenomenology, September 8, 2009. Christos Kokorelis. Based on : C.K, 0812.4804[hep-th] ; C.K , V.E.Mayes, D,V. Nanopoulos, 0907.4028 [hep-th ]. Basic Idea.
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Quark masses from Gaugino Condensation in String Theories Talk at Corfu Summer Institute, Theory-Cosmology-Phenomenology, September 8, 2009 Christos Kokorelis Based on : C.K, 0812.4804[hep-th]; C.K, V.E.Mayes, D,V. Nanopoulos, 0907.4028 [hep-th]
Basic Idea • Generate masses for all generations, reproduce hierarchical Q+L masses • Examples: Toroidal orientifolds IIA/IIB: 1 family get a mass, 2 massless one’s ≈ factorization of Yukawa’s ≈ 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
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]
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
PART I Missing mass terms for SU(5) Orientifold GUTS
Missing mass terms for u-quarks in orientifolds • SU(5)/FSU(5) GUTS in (IIA, IIB)/ΩR 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)
A typical SU(5) GUT Bachas, Blumenhagen, Kors, Lust, Ott, Ellis, Kanti, Nanopoulos, Axenides, C.K, Floratos, Bianchi, Weigand
Historical facts SU(5) GUT Flipped SU(5) GUT Yukawa mass terms SU(5) 10 10 5H = εijklm 10i 10j 5Hm = u c3 u3 <h0> Yukawa massterms FSU(5) 10 10 5H = εijklm 10i 10j 5Hm = dc3 d3 <h0>
Part II Perturbative solution to missing quark masses in SU(5), flipped SU(5) orientifolds
The coupling “exists” from charge and gauge invariance gets charged ~SU(5) x U(1) The or ~ SU(5) x Sp(2) x..
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 • <0|QL UR|0>= μ3 ~ (1,2)-1/2 Ibanez, Marchesano,Rabadan
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)) :
b<0 , ~ 0 1016 < Ms < 1018
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