F. Quevedo, On Local String Models and Moduli Stabilisation

511 views

Published on

Balkan Workshop BW2013
Beyond the Standard Models
25 – 29 April, 2013, Vrnjačka Banja, Serbia

Published in: Education, Technology, Business
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
511
On SlideShare
0
From Embeds
0
Number of Embeds
57
Actions
Shares
0
Downloads
0
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

F. Quevedo, On Local String Models and Moduli Stabilisation

  1. 1. Local String Models inCompact Calabi-YauManifolds and ModuliStabilisationF. Quevedo, ICTP/Cambridge.SEENET BW2013April 2013M.Cicoli, S. Krippendorf, C. Mayrhofer, FQ, R. Valandro:arXiv:1206.5237 + 1304.2771+ 1304.0022
  2. 2. Outline•  Introduction•  Overview of Local Models and LARGEvolume scenario•  Local Models in Compact Calabi-Yau(D3 and D3/D7 Models)•  The Web of Local Models
  3. 3. Introduction
  4. 4. Life After the Higgs?Hierarchy Problem Proposals•  TeV SUSY•  Warped extra dimensions•  Large extra dimensions•  Landscape...UV complete?How to break SUSY?How to fix size of extra dimensions?...
  5. 5. SUSY and String Theory•  Strings provide UV completion•  SUSY needed for consistency•  Scale of SUSY breaking?Sparticle masses: 10-3 eV,…TeV,...,< Mplanck !Disclaimer: Not necessarily at LHC scale!
  6. 6. Generic String Predictions•  Gravity + dilaton+antisymetric tensors+gauge fields + matter•  SUSY (32,16, … supercharges)•  Extra dimensions (6 or 7)(flat, small, large, warped?)•  Others? (branes, no csr, dualities,…)
  7. 7. Generic 4D String ‘Predictions’•  Moduli (s=0 ‘massless’ fields)•  Antisymmetric tensors:Branes (brane-world)Axions (not necessarily QCD axion)Quantised fluxes!•  If 4D N=1 SUSY: Cosmological ModuliProblem!? (Mmoduli>10 TeV)•  Only low-dimensional group representations.
  8. 8. Challenges for String Models•  Gauge and matter structure of SM•  Hierarchy of scales + masses (including neutrinos)•  Flavor CKM, PMNS mixing, CP no FCNC•  Hierarchy of gauge couplings (unification?)•  ‘Stable’ proton + baryogenesis•  Inflation or alternative for CMB fluctuations•  Dark matter (+ avoid overclosing)•  Dark radiation (Neff>3)•  Dark energyN.B. If ONE of them does not work, rule out the model!!!
  9. 9. Progress in past 10 years•  Model buildingLocal (branes at singularities, F-theory)Global (heterotic,…)•  Calculability !!!e.g.: Non-perturbtive effects (gauge and stringy)•  Moduli Stabilisation (landscape, inflation,…)
  10. 10. Model Building
  11. 11. String Model Building:§ Global Models (e.g. Heterotic)§ Local Brane Models (e.g. IIB)
  12. 12. Bottom-up Approach•  Gauge group•  Chiral spectrum•  Yukawa couplings•  Gauge couplings•  Proton stability•  Flavour symmetries•  Moduli Stabilisation•  Cosmological constant•  SUSY Breaking•  Scales (unification,axions,…)•  Inflation, Reheating•  Cosmological moduliproblemLocal (brane) Properties Global (bulk) PropertiesAldazabal,Ibanez, FQ, Uranga 2000
  13. 13. MODULI STABILISATION4-cycle size: τ(Kahler moduli)3-cycle size: U(Complex structuremoduli)+ String Dilaton: S4-cycle size: τ(Kahler moduli)3-cycle size: U(Complex structuremoduli)
  14. 14. Exponentially Large VolumesExponentially large volume + Broken SUSY!!!Kahler moduli:
  15. 15. 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
  16. 16. Original Scenarios•  MString = MGUT~ 1016 GeV (V~105)•  W0~10-11<<1 to get TeV soft terms, or W0~1 and 1010 GeV 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?
  17. 17. Visible orHiddenSectorsD3 BraneorD7 BraneWhere istheStandardModel?
  18. 18. LARGE Volume ImpliesStandard Model is localised !( SM D7 cannot wrap the exponentially large cyclesince g2=1/V2/3 ) ‘Bottom-up’ (AIQU 2000)§  D3/D7 Branes at a singularity (collapsed cycle)§  Magnetised D7 - Brane wrapping a ‘small’ four-cycle§  Local F-Theory
  19. 19. D3 Branes at Singularities• Orbifolds• Del Pezzos 0-8(dPn=P2 blown-up at n arbitrary pointsc1>0, b2=n+1, 2n-8 parameters, n>3)• Larger class: Toric singularities(infinite class of models!!!)
  20. 20. Spectrum and couplingsDimer and Quiver Diagrams (e.g. dP0)12 3
  21. 21. Del Pezzo Singularities/Quiverse.g. del Pezzo 0 (C3/Z3)ni D3 Branes (group ПU(ni))mj D7 Branes (group ПU(mi))Arrows=bi-fundamentalsAnomaly/tadpole cancelationHypercharge (ni≠nj)3 Families!D7s:Franco-Uranga
  22. 22. Standard Models LR-Symmetric ModelsPati-Salam Models Trinification Models
  23. 23. Problem for dP0: Yukawa couplingsE-values (M,M,0).From global flavour symmetry SU(3) (?)Del Pezzo1 SingularitySU(2)xU(1) Flavour symmetryConlon, Maharana, FQHierarchy in 3 generation masses!!!!Higgsing gives back dP0!!!
  24. 24. e.g. Realistic dP1 ModelsStandard Model LR Symmetric Model
  25. 25. Generic Features•  Approximate Flavour Symmetries•  Maximum number of families = 3 (toric)•  Quark Mass hierarchy: (M,m,0), M>>m•  Hyperweak Interactions(SM fields charged under D7 gaugeinteractions g2=1/V2/3 <<<1)Burgess et al. 2008Conlon, Maharana, FQ
  26. 26. Global Embedding andModuli StabilisationCicoli, Krippendorf,Mayrhofer, FQ, Valandro
  27. 27. Global Picture
  28. 28. Classification from ToricAmbient Spaces
  29. 29. Concrete (Compact) Calabi-Yauection we summarise the details of the CY manifold we already presented in [2]or the following analysis. The toric ambient variety into which the CY hypersumbedded is given by the following weight matrix:z1 z2 z3 z4 z5 z6 z7 z8 DeqX1 1 1 0 3 3 0 0 90 0 0 1 0 1 0 0 20 0 0 0 1 1 0 1 30 0 0 0 1 0 1 0 2,10tanley-Reisner ideal isSR = {z4 z6, z4 z7, z5 z7, z5 z8, z6 z8, z1 z2 z3} . (18the last column of the table indicates the degrees of the hypersurface equatione Hodge numbers of the CY are h1,1= 4 and h1,2= 112, such that χ = −216more, the three toric divisors D4, D7 and D8 are all P2, or dP0, on X and mutuallsecting.H1,1(X) we chose the basis8involutionorientifold involution that exchanges two of the three dP0 diviiteria are met if we choose the following involution:z4 ↔ z7 and z5 ↔ z6 ,he CY hypersurface X symmetric under this holomorphic invot its complex structure such that the defining equation eqX = 0nvolution. From (25) we see that the two dP0’s at z4 = 0 anan orientifold involution that exchanges two of the three dP0 divisore criteria are met if we choose the following involution:z4 ↔ z7 and z5 ↔ z6 ,e the CY hypersurface X symmetric under this holomorphic involuttrict its complex structure such that the defining equation eqX = 0 ise involution. From (25) we see that the two dP0’s at z4 = 0 andnged by the involution. Furthermore, in [2] we showed that the invaven by the following two orientifold planes:O7-planes Locus in ambient space Homology class in X3O71 : y6 = z4z5 − z6z7 = 0 DO71 = D6 + D7 = DbO72 : y5 = z8 = 0 DO72 = D8 = DsOrientifold
  30. 30. dP0 with only D3 Branes
  31. 31. Consistency Constraints•  Orientifolding induces orientifoldplanes with non zero 3-7 charges•  D7 tadpoles ✔•  D5 tadpoles ✔•  D3 tadpoles ✔•  Freed-Witten anomaly ✔•  K-theory charges ✔
  32. 32. Moduli StabilisationMinkowski vacuum, Ms=MGUT~1016 GeV,sequestered SUSY soft terms TeV (~1/V2).
  33. 33. Sequestered Scenario* No CMP,* No gravitino induced moduli problem,* Volume reheatingModel independent !MGUT~1016 GeV
  34. 34. dP0 D3 and Flavour D7 Branesset of values of ni to a different set.n2n0n1m1m0m2Figure 1: The dP0 quiver encoding the SU(n0) × SU(n1) × SU(n2) gauge theory with flavour branes.Potential D7-D7 states are not shown.2.2 Compact Models and constraints on local chargesfor flavourbranesWe now want to embed the local models on the dP0 singularity with D3 and flavour D7ocus on the simplest models based on the Z3 singularity or ro singularity dP0. The extended quiver diagram including flavgure 6. Each node with label ni corresponds to a U(ni) gaugebi-fundamental fields (ni, ¯nj). For each gauge group, a distThe ni denote the multiplicity of each fractional brane leadingoup U(ni). Given a choice of D3 brane gauge groups ni, the flam0, m1, m2 are constrained by anomaly cancellation:m0 = m + 3(n1 − n0) m1 = m m2 = m + 3(n1 − n2) .ing the number of D3 branes n0, n1, n2 in order to look for ae number of D7 branes up to a free integer m.2ple, choosing all D3-brane gauge groups to equal three n0 =Non-compact (local) case: m arbitraryCompact (global embedding): m is highly constrained!that the charge has to be a positive multiple of H.gives strong constraints on the numbers ni, mi for the locompact CY manifold:m ≥ 0 3(n1 − n0) + m ≥ 0 3(n1 − n2) + m ≥ 0 ,to0 ≤ −m ≤ 3(n1 − max{n0, n2}) .e.g. n0=n1=n2 implies m=0!!!
  35. 35. A LR-Model: Brane Set-upσπφχ+-χσ-++φ-dPdP 00D72flavD72flavD70flavD70flavD7SU(2) D7SU(2)re 3. Brane setup: The red points represent the fractional branes. There are two branes
  36. 36. Moduli Stabilisation4(yellow line), W0 = 10−7(purple line), W0 = 10−14(green line);this result into (3.34), we findV =W20V33ζ4g3/2s−32ln (V/W0)as3/2+ pV1/3[ln (V/W0)]2 .ng with respect to V we obtain=32ln (V/W0)as3/21 −12 ln (V/W0)−89pV1/3[ln (V/W0)]2 1 +34 ln (V/Wbstituted in (3.36) yields the following expression for the vacuum energyV =W20V 3lnVW0−34 a3/2s+p9V 1/3[ln (V/W0)]5/21 −6ln (V/W0).= π/3 and writing V = 10x, Figure 4 shows how the vacuum energy chanW0 = 10 (yellow line), W0 = 10 (purple line), W0 = 10 (green line);Plugging this result into (3.34), we findV =W20V33ζ4g3/2s−32ln (V/W0)as3/2+ pV1/3[ln (V/W0)]2 . (3Minimising with respect to V we obtain3ζ4g3/2s=32ln (V/W0)as3/21 −12 ln (V/W0)−89pV1/3[ln (V/W0)]2 1 +34 ln (V/W0)(3which substituted in (3.36) yields the following expression for the vacuum energyΛ ≡ V =W20V 3lnVW0−34 a3/2s+p9V 1/3[ln (V/W0)]5/21 −6ln (V/W0). (3Setting as = π/3 and writing V = 10x, Figure 4 shows how the vacuum energy changesfunction of x for different values of W0 at constant p (shown here for cσ = 1 and cφ = 1The preferred values of V and W0 are chosen in such a way to obtain a Minkowvacuum and TeV-scale supersymmetry at the same time. In the presence of flavour braPlugging this result into (3.34), we findV =W20V33ζ4g3/2s−32ln (V/W0)as3/2+ pV1/3[ln (V/W0)]2 .Minimising with respect to V we obtain3ζ4g3/2s=32ln (V/W0)as3/21 −12 ln (V/W0)−89pV1/3[ln (V/W0)]2 1 +34 ln (V/Wwhich substituted in (3.36) yields the following expression for the vacuum energyΛ ≡ V =W20V 3lnVW0−34 a3/2s+p9V 1/3[ln (V/W0)]5/21 −6ln (V/W0).Setting as = π/3 and writing V = 10x, Figure 4 shows how the vacuum energy chanunction of x for different values of W0 at constant p (shown here for cσ = 1 and cφThe preferred values of V and W0 are chosen in such a way to obtain a Mivacuum and TeV-scale supersymmetry at the same time. In the presence of flavouroop corrections to the visible sector gauge kinetic function might induce moduliTwo flux ‘parameters’: gs=1/65, W0=0.01Determine 4 physical quantities:Ms=1012 GeV, 1α = 20, Λ~0, Msoft~TeV(But CMP?).
  37. 37. UnificationMZ Mbreaking MStringΑ31Α21Αy110 1000 105 10710910111013x GeV20406080100Α 1
  38. 38. Web of Quiver Models
  39. 39. Quiver Transitionsuntil it splits into a brane wrapping (1+αb)Db −Dq1 and one wrapping Dq1 ; if this last branehas the suitable flux such that its charge vector is minus the charge vector of one of thefractional branes, then it annihilates with it, lowering the corresponding multiplicity ni. Aswe can already see from the D7-charge, the only fractional branes that can be annihilatedare F0 and F2 because they have the charge of an anti-D7-brane wrapping Dq1 .3333231Figure 3: Transition from the SU(3)3quiver to the SU(3)2× SU(2): One D7-brane (solid green line)on top of the O-plane (dotted line) splits into a flavour brane intersecting the fractional branes (red andblue lines) and into an anti-fractional brane. This last one annihilates one fractional brane from the red
  40. 40. Transitions continuuing3333112 2...Figure 4: By repeating four times the transition described in Figure 3, we get four flavour branes and noD7-brane on top of the O-plane.
  41. 41. Web of Quiver Models
  42. 42. CONCLUSIONS•  Continuous progress on local stringmodels•  Several SUSY breaking scenarios•  Local models: Global embedding andModuli Stabilisation!!!ü  Most local models not global embeddingü  Those that have form a web•  Most known ingredients used: geometry,fluxes, branes, perturbative, non-perturbative effects•  Many open questions
  43. 43. ICTPTrieste, ItalyAugust 26-31 2013susy2013.ictp.it
  44. 44. Dark RadiationEnergy density:At CMB: WMAP, ACT, SPTStandard Model Neff=3.04
  45. 45. Volume ReheatingVolume axion abClosed string axionsHiggsesMatter scalars CSimplest:General: Strong constraints onmatter and couplings!
  46. 46. SM Cycle does not break SUSY!‘Fayet-Iliopoulos’ à0‘Sequestered moduli/gravity mediated SUSY Breaking’No-scale (vanishing soft terms) Suppressed !
  47. 47. Sequestered Scenario* No CMP,* No gravitino induced moduli problem,* Volume reheatingModel independent !MGUT~1016 GeV
  48. 48. Higher del PezzosTriplication of families very limitedIn general most quivers k<4 arrowsFor dP8 model, seeH.Verlinde, M.Wijnholt (+Buican, Malyshev, Morrison) 06,07
  49. 49. ‘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
  50. 50. 333122322222211223

×