1. Quark masses from Gaugino Condensation in String Theories Christos Kokorelis Based on : C.K, 0812.4804[hep-th] ; C.K, V.E.Mayes, D,V. Nanopoulos, 0907.4028 [hep-th ] Talk at Corfu Summer Institute, Theory- Cosmology-Phenomenology, September 8, 2009

2. Basic Idea Generate masses for all generations, reproduce hierarchical Q+L masses Generate masses for all generations, reproduce hierarchical Q+L masses Examples: Toroidal orientifolds IIA/IIB: Examples: Toroidal orientifolds IIA/IIB: 1 family get a mass, 2 massless one’s ≈ factorization of Yukawa’s ≈ Non-zero I ab in 2 different tori [Cremades, Ibanez, Marchesano] 1 family get a mass, 2 massless one’s ≈ factorization of Yukawa’s ≈ Non-zero I ab in 2 different tori [Cremades, Ibanez, Marchesano] Additional Higgs evade the problem for specific values Additional Higgs evade the problem for specific values of the moduli [Cvetic, Langacker, Shiu, Chen, Li, Mayes, Nanopoulos] in Pati-Salam GUTS 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 SU(4) c x SU(2) L x SU(2) R like D-brane string models

3. 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]

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

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

6. 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 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 10 (2, 0) 10 (2, 0) 5 H (1, 1) A typical SU(5)/FSU(5) U/D quark mass term : A typical SU(5)/FSU(5) U/D quark mass term :

7. A typical SU(5) GUT Bachas, Blumenhagen, Kors, Lust, Ott, Ellis, Kanti, Nanopoulos, Axenides, C.K, Floratos, Bianchi, Weigand

8. Historical facts SU(5) GUT Flipped SU(5) GUT Yukawa mass terms SU(5) 10 10 5 H = ε ijklm 10 i 10 j 5 Hm = u c3 u 3 Yukawa mass terms FSU(5) 10 10 5 H = ε ijklm 10 i 10 j 5 Hm = d c3 d 3

9. Part II Perturbative solution to missing quark masses in SU(5), flipped SU(5) orientifolds

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

11. The In the case of chiral symmetry breaking as SU(3) symmetry is not spontaneously broken we take the vacuum to be SU(3) symmetric In the case of chiral symmetry breaking as SU(3) symmetry is not spontaneously broken we take the vacuum to be SU(3) symmetric = μ 3 ~ (1,2 )- 1/2 = μ 3 ~ (1,2 )- 1/2 condenses Ibanez, Marchesano,Rabadan

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

13. Sp(2) strongly coupled

14. b<0, ~ 0 10 16 < Ms < 10 18

15. 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