Phenomenological Aspects of Local String Models

Transcription

1 Phenomenological Aspects of Local String Models F. Quevedo, Cambridge/ICTP. PASCOS-2011, Cambridge. M. Dolan, S. Krippendorf, FQ; arxiv: S. Krippendorf, M. Dolan, A. Maharana, FQ; arxiv: C. Burgess, A. Maharana, FQ; arxiv: C. Burgess, M. Cicoli, M. Gomez-Reino, FQ, G. Tasinato, I. Zavala; arxiv

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

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

4 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,

5 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!!!

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

7 Bottom-up Approach Local (brane) Properties Gauge group Chiral spectrum Yukawa couplings Gauge couplings Proton stability Flavour symmetries Global (bulk) Properties Moduli Stabilisation Cosmological constant SUSY Breaking Scales (unification, axions, ) Inflation, Reheating Cosmological moduli problem

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

9 LARGE Volume Scenario

10 Exponentially Large Volumes Example : Perturbative (alpha ) corrections to K Fluxes Volume Nonperturbative corrections to W Exponentially large volumen + Broken SUSY!!!

11 e.g.swiss Cheese Calabi-Yau s Very generic Blumenhagen, et al., Grimm et al., Kreuzer et al. 08

12 e.g.: Anisotropic Moduli Fixing K3 Fibrations: Poly-Instantons Blumenhagen et al. K3! size t 2 2 i=3, j=1

13 (For W 0 =10, g s =0.01, etc.) Living on the edge!!

14 Relevant Scales String scale Ms=M P /V 1/2 Kaluza-Klein scale M KK =M P /V 2/3 Gravitino mass m 3/2 =W 0 M P /V Volume modulus mass M V =M p /V 3/2 Lighter (fibre) moduli M l =M p /V 5/3

15 Question: Unnaturally light scalars?

16 Loop induced heavy masses Without SUSY With SUSY Übernaturalness

17 General Scenarios M String = M GUT ~ GeV (V~10 5 ) W 0 ~10-11 <<1 (or W 0 ~1 plus warping) to get TeV soft terms Fits with coupling unification Natural scale of most string inflation models. Axi-volume quintessence scale (w= ) M String = M int. ~ GeV (V~10 15 ) W 0 ~1 m 3/2 ~1 TeV (solves hierarchy problem!!!) QCD axion scale neutrino masses LLHH M String = 1 TeV (V~10 30 ) W 0 ~1 Most exciting, 5th Force OK m~10-3 ev, if SM non SUSY. Back reaction?

18 Cosmological Inflation

19 Kähler Moduli Inflation (Blow-up) ~ Small field inflation (r<<<1) No fine-tuning!! 0.960<n<0.967 Loop corrections?? volume V τ n

20 Fibre Inflatons Burgess, Cicoli, FQ V

21 n s r r N e n s Observable gravity waves! (can be ruled out by Planck if they observe them and CMBpol if they do not observe them)

22 Stringy Curvaton Scenario

23 Curvaton Mass: Non-Gaussianities Examples

24 Model Building

25 LARGE Volume Implies Standard Model is localised! ( SM D7 cannot wrap the exponentially large cycle since g 2 =1/V 2/3 ) Bottom-up (AIQU 2000) Aldazabal et al. Fractional D3/D7 Brane at a singularity (collapsed cycle) Magnetised D7 - Brane wrapping a small four-cycle Local F-Theory Blumenhagen et al. Donagi, Wijnholt; Vafa, Heckman,

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27 D3 Branes at Singularities Orbifolds Del Pezzos 0-8 (dpn=p 2 blown-up at n arbitrary points c 1 >0, b 2 =n+1, 2n-8 parameters, n>3) Larger class: Toric singularities (infinite class of models!!!)

28 Toric Singularities Einstein-Sasaki T 3 Fibration Over rational polyhedral cone D3-branes Toric Diagram

29 Spectrum and couplings Dimer and Quiver Diagrams (e.g. dp0)

30 Del Pezzo Singularities/Quivers e.g. del Pezzo 0 (C 3 /Z 3 ) n i D3 Branes (group ПU(n i )) m j D7 Branes (group ПU(m i )) Arrows=bi-fundamentals 3 Families! Anomaly/tadpole cancelation D7s:Franco-Uranga Hypercharge (n i n j )

31 Standard Models LR-Symmetric Models Pati-Salam Models Trinification Models

32 General Results Toric 1.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)

33 Generic Features Aproximate Flavour Symmetries Hyperweak Interactions (SM fields charged under D7 gauge interactions g 2 =1/V 2/3 <<<1, CDF?) Burgess et al Conlon, Maharana, FQ

34 The Needle on a Haystack (search with a magnet!) Not simple GUT groups (SU(5), SO(10), ) Search for PS, LR, SM, Many U(1) s but if U(1) Y = Σ i U(1) i, wrong normalisation for MSSM unification (5/3). Also keep hypercharge massless in compact case. Then U(1) Y in G non-abelian (SU(4), ) ALL SM in D3 s at least G=PS, SU(3) 3

35 Minimal del Pezzo? dp0 no hierarchy of masses (unless noncommutative), no CKM dp1, dp2 no CKM or PMNS, no control of kinetic terms (FCNC?). dp3 flavor diagonal kinetic terms and realistic CKM, PMNS matrices.

36 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

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39 Quarks+leptons

40 CKM Matrix PMNS Matrix 14 Parameters vs 21 Observables

41 Gauge Coupling Unification String scale value of all couplings given by dilaton so unification. Standard GUT scale unification or intermediate scale Ms>10 12 GeV Need moduli stabilisation to fix scales.. (Large volume scenarios?...)

42 SUSY BREAKING

43 SUSY Breaking Approximate Universality CAQS, Conlon (Mirror Mediation) Two cases: F SM 0 soft terms~m 3/2 Ms~10 12 GeV F SM =0 soft terms <<m 3/2 or~m 3/2

44 CONCLUSIONS Continuous progress on local string models (TeV warping, TeV gravity, TeV SUSY!?) Several SUSY breaking scenarios (m~m 3/2, m 3/2 3/2 /M p 1/2, m 3/22 /M p ), (M s ~ GeV) Local model building (dp3: 3-families, mass hierarchies (M,m,0), CKM, PMNS, Unification, proton stable, ) Concrete models of inflation (gravity waves and non-gaussianities) Many open questions