1. Meta-stable Supersymmetry Breaking in Spontaneously Broken N=2 SQCD Shin Sasaki (Univ. of Helsinki) [hep-th/0708.0668 (M.Arai, C.Montonen, N.Okada and S.S)]

2. Introduction— meta-stable SUSY breaking Dynamical SUSY breaking  hierarchy problem can be solved Witten index  highly constrained models are allowed  very restricted models are considered before the discovery of the ISS model Witten index never restrict the possibility of meta- stable SUSY breaking vacua [Intriligator-Seiberg-Shih (2006)]

3. The ISS model SQCD with massive flavors IR-free magnetic dual One-loop up-lifting of pseudo moduli Long-lived local minimum Dynamical SUSY restoration Perturbative region Non-pertrubative SUSY restroation [Intriligator-Seiberg-Shih (2006)]

4. Ubiquity of meta-stable SUSY breaking ISS inspired model Perturbed Seiberg-Witten Brane constraction U(1)_R breaking Gauge mediation, finite temperature …. [Ooguri-Ookouchi-Park (2007), Pastras (2007)] [Shih (2007), Ferretti (2007), Intriligator-Seiberg-Shih (2007), …] [Franco-Garcia-Etxebarria-Uranga (2006), Ahn (2007), Ooguri-Ookouchi (2007), Eto-Hashimoto-Terashima (2007), Bena-Gorbatov-Hellerman-Seiberg-Shih (2007), Marsano-Papadodimas-Shigemori (2007) …] [Amariti-Girardello-Mariotti (2007), Essig-Sinha-Torroba (2007), Abel-Khoze (2007), …] [Kawano-Ooguri-Ookouchi (2007), Murayama-Nomura (2007),Aharony-Seiberg (2007), Kitano-Ooguri-Ookouchi (2007), …]

5. Plan of this talk Introduction Spontaneously broken N=2 SQCD Quantum theory Local minimum – numerical analysis Possible application to phenomenology Summary and future works

6. Spontaneous broken N=2 SQCD gauge theory with hypermultiplets and FI-term (D-term) The simplest case  Global symmetry

7. Pseudo flat direction Solution of stationary condition of the potential SUSY is broken at tree-level Pseudo flat direction Gauge symmetry U(1)_R is broken

8. Quantum theory Effective action FI term is tree-level exact [Arai-Kitazawa (1999)] Harmonic superspace analysis, gauge symmetry, U(1)_R charge…. Coulomb branch U(1) gauge theory  cutoff theory, Landau pole Seiberg-Witten analysis, Long-lived local minimum [Arai-Okada (2001)]

9. SUSY effective action Vector multiplet part Light BPS states around singular points M corresponds to dyons, monopoles, quarks Spinor representation of [Seiberg-Witten (1994)]

10. Prepotential Moduli space Monodoromy transf.  subgroup of Same structure with massive SQCD (common quark hypermultiplet mass) is regarded as the mass

11. Potential Stationary points  Singular points : energetically favored !

12. Solution SW curve Meromorphic differential Periods

13. Explicit form (Weierstrass functions, elliptic integrals)

14. U(1) sector

15. Local mininum Flow of singularities

16. Dyon points Increasing direction Re(a_1) direction

17. Im(a_1) direction

18. Local mininum at a_1 = 0 Local minimum at SUSY and global U(1)_R are broken !

19. Local minimum SUSY breaking and U(1)_R breaking Runaway direction

20. Decay rate estimate Long-lived vacuum [Dancan-Jensen (1992)]

21. Application to phenomenology SUSY breaking effect  gauge mediation Messenger sector Gaugino mass Singular point in moduli space (meta-stable vacuum)

22. Summary gauge theory with hypermultiplets and FI-term We have found a meta-stable vacuum in which SUSY and U(1)_R are dynamically broken (non-perturbative) Long-lived local minimum with runaway SUSY vacuum The model naturally contains messenger sector of gauge mediation

23. Future works Generalize to arbitrary Geometric realization of the meta-stable vacua : NS5/D4/(D6)  M5 (with TN) Embedding the Standard Model gauge symmetry into the flavor symmetry Finite temperature correction