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The LARGE Volume String Scenarios

The LARGE Volume String Scenarios. F. Quevedo, Cambridge/ICTP. Havana, Cuba 2012. J. Conlon, V. Balasubramanian, P. Berglund, FQ +….since 2005 M. Dolan, S. Krippendorf, FQ; arXiv:1106… S. Krippendorf, M. Dolan, A. Maharana, FQ; arXiv:1002.1790 C. Burgess, A. Maharana, FQ; arXiv:1005.1199

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The LARGE Volume String Scenarios

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  1. The LARGE Volume String Scenarios F. Quevedo, Cambridge/ICTP. Havana, Cuba 2012. J. Conlon, V. Balasubramanian, P. Berglund, FQ +….since 2005 M. Dolan, S. Krippendorf, FQ; arXiv:1106… S. Krippendorf, M. Dolan, A. Maharana, FQ; arXiv:1002.1790 C. Burgess, A. Maharana, FQ; arXiv:1005.1199 C. Burgess, M. Cicoli, M. Gomez-Reino, FQ, G. Tasinato, I. Zavala; arXiv1005.4840 M.Cicoli, S. Krippendorf, C. Mayrhofer, FQ, R. Valandro; arXiv1206.5237

  2. Recall LHC is running: Hierarchy Problem Proposals • TeV SUSY • Warped extra dimensions • Large extra dimensions • … UV complete? How to fix size of extra dimensions? Unification, Flavour, Proton stability,…

  3. String Theory • Particles ‘look like’ strings • (Super) Gravity is included • Can unify all particles and interactions (Einstein’s dream) • Universe lives in 10 (11) dimensions !!! • For our universe 10d = 4d+6d (6d very small?) • Dimensionful scale: Ms. • Many couplings: Moduli (1/g2=T)

  4. String Phenomenologists:Strategic (long term) Plan:String theory scenario that satisfies all particle physics and cosmological observations and hopefully lead to measurable predictions

  5. String Phenomenology • Too many string models? (Heterotic, IIA, I, IIB, Landscape,...) • Or too ‘few’ models? (Realistic?)

  6. Challenges for String Models • Gauge and matter structure of SM • Hierarchy of masses (including neutrinos) • Flavor CKM, PMNS mixing, CP no FCNC • Hierarchy of gauge couplings (unification?) • ‘Stable’ proton + baryogenesis • Dark matter (+ avoid overclosing) • Inflation or alternative for CMB fluctuations • Dark energy N.B. If ONE of them does not work, rule out the model!!!

  7. String Model Building: • Global Models (e.g. Heterotic) • Local Brane Models (e.g. IIB)

  8. Gauge group Chiral spectrum Yukawa couplings Gauge couplings Proton stability Flavour symmetries Moduli Stabilisation Cosmological constant SUSY Breaking Scales (unification, axions,…) Inflation, Reheating Cosmological moduli problem Bottom-up Approach Aldazabal,Ibanez, FQ, Uranga 2000 Local (brane) Properties Global (bulk) Properties

  9. MODULI STABILISATION 4-cycle size: τ (Kahler moduli) 3-cycle size: U (Complex structure moduli) + String Dilaton: S

  10. LARGE Volume Scenario

  11. Type IIB String on Calabi-Yau orientifold Turn on Fluxes ∫aF3 = n a ∫bH3 = m b SuperpotentialW = ∫ G3ΛΩ, G3 = F3 –iSH3 Scalar Potential:V= eK |DaW|2 MinimumDaW = 0Fixes Ua and S T moduli unfixed: No-Scale models IIB Moduli Stabilisation …GKP, KKLT, … Size of cycle a = Ua GKP

  12. Kahler moduli?Simple example:P411169

  13. Exponentially Large Volumes BBCQ, CQS (2005) Example : Perturbative (alpha’) corrections to K Volume Nonperturbative corrections to W Fluxes Exponentially large volumen + Broken SUSY!!!

  14. General Conditions for LARGE Volume • h12 > h11 > 1 • At least one blow-up mode (point-like singularity) • Blow-up mode fixed by non-perturbative effects, volume by alpha’ corrections, other (fibre) by loop corrections. Cicoli, Conlon, FQ

  15. e.g.Swiss Cheese Calabi-Yau’s Very generic Blumenhagen, et al., Grimm et al., Kreuzer et al. 08

  16. e.g.: Anisotropic Moduli Fixing • K3 Fibrations: Poly-Instantons Blumenhagen et al. K3 ! size t22 i=3, j=1

  17. (For W0=10, g s=0.01, etc.) Living on the edge!!

  18. Relevant Scales • String scale Ms=MP/V 1/2 • Kaluza-Klein scale MKK=MP/V 2/3 • Gravitino mass m3/2=W0 MP/V • Volume modulus mass MV=Mp/V 3/2 • Lighter (fibre) moduli Ml=Mp/V 5/3

  19. General Scenarios • MString = MGUT~ 1016 GeV (V~105) • W0~10-11<<1 (or W0~1 plus warping) to get TeV soft terms • Fits with coupling unification • Natural scale of most string inflation models. • Axi-volume quintessence scale (w=-0.999….) • MString = Mint.~ 1012 GeV (V~1015) • W0~1 • m3/2~1 TeV (solves hierarchy problem!!!) • QCD axion scale • neutrino masses LLHH • MString = 1 TeV(V~1030) • W0~1 • Most exciting, 5th Force OK m~10-3 eV, if SM non SUSY. Back reaction?

  20. Cosmological Inflation

  21. Kähler Moduli Inflation (Blow-up) Conlon-FQ Bond et al. … ~ Calabi-Yau: h21>h11>2 V Small field inflation (r<<<1) No fine-tuning!! 0.960<n<0.967 Loop corrections?? τn volume

  22. Fibre Inflatons Burgess, Cicoli, FQ V

  23. ns r r Ne ns Observable gravity waves ! (can be ruled out by Planck if they observe them and CMBpol… if they do not observe them)

  24. Stringy Curvaton Scenario

  25. Curvaton Mass: Non-Gaussianities Examples

  26. Model Building

  27. LARGE Volume Implies Standard Model is localised ! ( SM D7 cannot wrap the exponentially large cycle since g2=1/V2/3 ) ‘Bottom-up’ (AIQU 2000) • Fractional D3/D7 Brane at a singularity (collapsed cycle) • Magnetised D7 - Brane wrapping a ‘small’ four-cycle • Local F-Theory Aldazabal et al. Blumenhagen et al. Donagi, Wijnholt; Vafa, Heckman, …

  28. Universe D3 Brane or D7 Brane

  29. D3 Branes at Singularities Orbifolds Del Pezzos 0-8 (dPn=P2 blown-up at n arbitrary points c1>0, b2=n+1, 2n-8 parameters, n>3) Larger class: Toric singularities (infinite class of models!!!)

  30. Toric Singularities Einstein-Sasaki T3 Fibration Over rational polyhedral cone D3-branes Toric Diagram

  31. Spectrum and couplings Dimer and Quiver Diagrams (e.g. dP0)

  32. Del Pezzo Singularities/Quivers e.g. del Pezzo 0 (C3/Z3) ni D3 Branes (group ПU(ni)) mj D7 Branes (group ПU(mi)) Arrows=bi-fundamentals 3 Families! Anomaly/tadpole cancelation Hypercharge (ni≠nj) D7s:Franco-Uranga

  33. Standard Models LR-Symmetric Models Trinification Models Pati-Salam Models

  34. General Results Toric Maximum number of families = 3 (except for one case F0 with 4 families, dual to a 2-family model, also non-toric phases unbounded) 2. Quark Mass hierarchy: (M,m,0) with M>>m (structure of Yukawas imply one zero e-value, only dP0 has m=M)

  35. ‘Realistic’ ‘Pati-Salam’ Model (dP3) • Break symmetry to SM (+ U(1) or LR) • Breaking U(1) to SM: RH sneutrino (R-parity broken) • Quark+ lepton mass hierarchies • See-saw neutrino masses • Stable proton • CKM, CP • Controlled kinetic terms!! !!! • Gauge Unification

  36. Generic Features • Approximate Flavour Symmetries • Hyperweak Interactions (SM fields charged under D7 gauge interactions g2=1/V2/3 <<<1) Burgess et al. 2008 Conlon, Maharana, FQ

  37. SUSY BREAKING

  38. SUSY Breaking • Approximate Universality • Two cases: FSM≠0 soft terms~m3/2 Ms~1012 GeV FSM=0 soft terms <<m3/2 or~m3/2 CAQS, Conlon (Mirror Mediation)

  39. SM Cycle does not break SUSY ‘Fayet-Iliopoulos’ 0 ‘Sequestered moduli/gravity mediated SUSY Breaking’ No-scale (vanishing soft terms) Suppressed !

  40. Different Scenarios • Scalars 1/V3/2, others 1/V2 • All a/V3/2 • All 1/V2 (No CMP, unification, inflation !!!) • Loop corrections ~ b/V5/3 • Mstring~1013-1015 GeV • Field redefinitions at loop order: soft terms 1/V except ‘ultra-local’ SM at D3.

  41. Global Embedding and Moduli Stabilisation

  42. Global Picture

  43. Classification from Toric Ambient Spaces

  44. Consistency Constraints • Orientifolding induces orientifold planes with non zero 3-7 charges • D7 tadpoles • D5 tadpoles • D3 tadpoles • Freed-Witten anomaly • K-theory charges

  45. dP0 (ultra-local)Trinification

  46. dPn ultra local

  47. Moduli Stabilisation

  48. CONCLUSIONS • Continuous progress on local string models (TeV warping, TeV gravity, TeV SUSY,…!?) • Several SUSY breaking scenarios (m~m3/2, m3/23/2/Mp1/2, m3/22/Mp ), (Ms~103 – 1016 GeV) • Concrete models of inflation (gravity waves and non-gaussianities) • Local models: Global embedding and Moduli Stabilisation!!! • All known ingredients used: geometry, fluxes, branes, perturbative, non-perturbative effects • Many open questions

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