1. 超弦理論的現象論 山口 昌弘 （東北大学） 研究会 超弦理論と宇宙＠尾道 ２００８年 2 月１１～ 13 日

2. 2 Talk Plan Introduction : Flux compactification and KKLT set-up Naturalness Problem of Weak Scale Warped Superstring Compactification SUSY phenomenology: mirage mediation

3. 3 String Theory Candidates for 1) Quantum Gravity 2) Ultimate Unified Theory –gauge structure –matter representations –generations –Yukawa couplings They are sensitive to details of compactification. Probably premature….. –origin of weak scale supersymmetry breaking/ warped extra dimensions … To me, this is less sensitive to details of compactification. Hope to get some insight.  I will discuss possible implications to TeV scale physics. “String (inspired) phenomenology”

4. 4 Moduli Stabilization: A long-standing problem Moduli/Dilaton Stabilization –Moduli have not been stabilized at tree level. –Non-perturbative effects important Why moduli? –structure of compact dimensions –gauge & matter structure if light moduli –SUSY breaking –Cosmological implications

5. 5 Gaugino condenstate: runnaway potential exponetial superpotential  runaway scalar potential How to avoid runaway? race track : multiple gaugino condensates non-perturbative corrections to Kaehler potential ……… V Re S

6. 6 Flux Compactificatons Switch on Fluxes: H (3) and F (3) type IIB side Consistent solution Complex moduli & dilaton are stabilized

7. 7 IIB superstring –2-form potential (NS-NS, RR) –3-form field strength superpotential for IIB theory complex moduli quantization of fluxes (3,0) form Gukov-Vafa-Witten ’99

8. 8  superpotential for complex moduli (z) and dilaton (  ) Consistent solution for flux compactifications in IIB –fluxes  warped throat (Klebanov-Strassler throat) –W stabilizes complex moduli as well as dilaton –Kaehler moduli are not stabilized by fluxes Giddings-Kachru- Polchinski 02

9. 9 KKLT set-up Potential for Kaehler moduli:  non-perturbative effects e.g. gaugino condensate on D7 brane case of single overall moduli: gauge kinetic function on D7: superpotential from gaugino condensate Kachru-Kallosh-Linde-Trivedi 03

10. 10 Constant term in Superpotential  simplest way to avoid runnaway behavior T modulus stablilized but with SUSY AdS vacuum (Re T)

11. 11 Up-lifting of the scalar potential –Adding SUSY breaking sector –Minkowski, SUSY broken vacuum –KKLT: anti-D3 on top of warped throat – Dynamical SUSY breaking sector on D-branes can also be OK (Re T)

12. 12 Naturalness of Weak Scale Why is weak scale much smaller than Planck scale? How is weak scale stabilized against radiative corrections? Proposed Solutions: –Low energy supersymmetry –Large/Warped extra dimensions –Unknown strong dynamics ….. Ingredients in string theory. Question is which plays a crucial role.

13. 13 KKLT: A Platform of TeV Phenomenology Warped Extra Dimension & Low Energy SUSY Similar set-up with different flux configurations and SM- brane configuration Macroscopically (phenomenologically) important information: w_0, warp factor  warped extra dim. and low-E SUSY large w_0 strong warping small w_0 mild warping

14. 14 LHC (Large Hadron Collider) Experiment pp collider at CERN Center of mass energy =14 TeV Starts 2008 (this year!) Expects new physics discovery at TeV scale

15. 15 Warped Superstring Compactification at LHC Noguchi, Yamashita &MY 04 Shiu et al 07 Yamashita, 08

16. 16 Warped Extra Dimension 4+1 spacetime theory gives a solution to the large hierarchy –The extra dimension with finite size –Massive objects A pair of branes with opposite tension Cosmological constant –SM-brane is located at a end of the extra dimension Solution is AdS5 Randall-Sundrum (’99) Warp factor SM-Brane SM metric with Poincare symmetry

17. 17 A stringy realization Giddings-Kachru-Polchinski ‘02 Use of Klebanov-Strassler (KS) geometry –Deformed conifold KS throat is glued into some CY to give finite 4D gravity

18. 18/13 How do we learn geometry of WED ? –Kaluza-Klein modes: function on extra dimension manifold  Properties of manifold Kaluza-Klein (KK) modes –Gravitational field propagates extra dimensions: KK modes as a probe of extra dimensions –Momentum along extra dim.  KK Mass –Amplitude  KK couplings to SM-brane Wavefunction of KK mode: localized nearby IR region –sensitive to IR properties of warped throat

19. 19/13 KK modes can be observed at collider experiments –Seen as resonances in Drell-Yan process –Resonance: position, width, height  Mass, coupling etc cf. Davoudiasl et al. (2000)

20. 20/13 Warped superstring solution in type-IIB superstring: Manifold is of Planck-size volume –Realistic gravitational coupling KS-throat glued to a CY-space The warped metric generated by anti-symmetric F3 and H3 –Supersymmetry –Moduli stabilization Standard model brane at the apex of the conifold Warped Extra Dimensions À La String Theory Giddings, et al. (’03) Klebanov-Strassler (2000) KS-Throat SM-Brane

21. 21/13 Deformed Conifold Conical 6 dimensional manifold –The singularity is removed by with finite size S^3 – as its intersection –S^3 squashes as tau grows Warped Extra Dimensions À La String Theory SM-brane Infrared (IR) Ultra- violet (UV)

22. 22/13 Warping generated by fluxes –F3 going through S^3 –  H3 and F5 generated From the solution for Einstein’s Eq. –Poincare symmetry on SM-brane –Warp factor is asymptotically AdS ( : Dilaton VEV, : String length) Warped Extra Dimensions À La String Theory SM metric with Poincare symmetry Warp factor KS AdS Radial dependence of warp factor SM-brane located here

23. 23/13 Angular direction for extra dim. Where One-forms for angular coordinates Deformation Parameter, determined by flux ratio Warped Extra Dimensions À La String Theory Angular directions Angular directions

24. 24/13 Form of the Wave functions 1 st Mode 2 nd Mode 5 th Mode

25. 25/13 Numerical Results Mass and coupling for angular modes

26. 26 Comparison with RS model Coupling Universality is Violated in stringy realization Mass spectrum is busier. Two geometries are distinguishable experimentally. KK modes are sensitive probe of IR region of warped throat.

27. 27 Implication to Low E SUSY

28. 28 Implications to Low-E SUSY Original Motivation of KKLT: realization of dS vacuum in string theory Simple KKLT set-up can also provide a new mediation mechanism of SUSY breaking. mixed modulus anomaly mediation = mirage mediation Choi-Falkowski-Nilles -Olechowski-Pokorski 04,05 Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05.........

29. 29 Phenomenology with KKLT-like model SUSY breaking sector added to uplift potential Overall SUSY breaking characterized by gravitino mass: SUSY breaking effect of Moduli T: suppressed by one-loop factor

30. 30 Gaugino Masses @GUT scale moduli+anomaly mediation: two contributions comparable Consider SM on D7 brane Gauge kinetic function Gaugino Mass

31. 31 Gaugino Masses For R~35 (KKLT), M 1 : M 2 : M 3 ~1 : 1.3: 2 cf. M 1 : M 2 : M 3 ~1: 2: 7 (mSUGRA)

32. 32 Mirage Mediation RG properties: Gaugino masses (as well as scalar masses) are unified at a mirage scale. Choi, Jeong, Okumura 05 from Lebedev, Nilles, Ratz 05

33. 33 General Features of Mirage Mediation Compact Sparticle Mass Spectrum small  parameter (~M 1 )  small gluino mass/ RGE LSP(lightest superparticle): neutralino –admixture of gauginos and higginos stau: tends to be light Mass Spectrum is very different from mSUGRA (CMSSM), gauge mediation & anomaly mediation Testable at future collider experiments (LHC/ILC) Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05

34. 34 Mass Spectrum: Case Study n=1,l=1/3n=3,l=0 (KKLT) Endo,MY,Yoshioka 05

35. 35 Cosmological Embarrassment? Gravitino Over-Production Moduli is relatively heavy ~10 7 GeV  no cosmological moduli problem…? Gravitino is also heavy ~10 5 GeV  no gravitino problem …? However, “Gravitino Over-Production by Moduli Decay”

36. 36 Gravitino Pair Production by Moduli Decay Br(X  G 3/2 G 3/2 ) ~0.01 –essentially decay into “Goldstinos” –proportional to Fx (SUSY breaking of X) –effect overlooked for more than 10 years (contribution suppressed for minimal Kaehler potential) BBN is OK if gravitino mass is heavier than ~ 50 TeV Most serious is over-abundance of neutralino DM produced by gravitino decay Endo,Hamaguchi, Takahashi 06 Nakamura&MY 06

37. 37 LSP abundance case study: LSP=neutral Wino (largest annihilation cross section) Gravitino mass must be heavier than ~10 6 GeV to escape overclosure constraint. (wino case) Even severer constraint on gravitino mass for other neutralino case Low energy SUSY might be disfavored in the presence of moduli. (unstable gravitino) Nakamura-MY 06

38. 38 Ways Out? lighter LSP (such as axino) –how to realize lighter LSP? in particular within modulus-anomaly mediation  Nakamura-Okumura-MY, to appear Stable Gravitino: (Asaka,Nakamura&MY 06) –Constraint on gravitino relic abundance: less constrained –possibility of gravitino warm dark matter –give up moduli-anomaly mediation? Dilution by entropy productionthermal inflation (Lyth & Stewart 96) Raising Gravitino Mass by Warped Configuration (Luty) –AMSB may be suppressed by warped factor –sensitive to radion stabilization –light radion?  may cause another cosmological trouble To overcome the moduli-induced gravitino problem is crucial for mixed moduli anomaly mediation (mirage mediation) under investigation….

39. 39 Conclusions Moduli Stabilization: Flux compactification Implications to Weak Scale Stabilization warped superstring compactification low-E SUSY: mirage mediation LHC will provide crucial information beyond SM, and hopefully structure of unified theory.

40. 40 Stay Tuned!