Phenomenological Aspects of Local String Models

F. Quevedo, Cambridge/ICTP. PASCOS-2011, Cambridge.

M. Dolan, S. Krippendorf, FQ; arXiv:1106.6039 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

String Phenomenologists:

Strategic (long term) Plan: String theory scenario that satisfies

all particle physics and cosmological observations and

hopefully lead to measurable predictions

String Phenomenology

•  Too many string models? (Heterotic, IIA, I, IIB, Landscape,...)

•  Or too ‘few’ models? (Realistic?)

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,…

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!!!

String Model Building:  Global Models (e.g. Heterotic)

 Local Brane Models (e.g. IIB)

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 moduli

problem

Local (brane) Properties Global (bulk) Properties

MODULI STABILISATION

4-cycle size: τ (Kahler moduli)

3-cycle size: U (Complex structure moduli)

+ String Dilaton: S

LARGE Volume Scenario

Exponentially Large Volumes Example :

Exponentially large volumen + Broken SUSY!!!

Fluxes

Volume

Perturbative (alpha’) corrections to K

Nonperturbative corrections to W

e.g.Swiss Cheese Calabi-Yau’s

Very generic

Blumenhagen, et al., Grimm et al., Kreuzer et al. 08

e.g.: Anisotropic Moduli Fixing •  K3 Fibrations:

Poly-Instantons

K3 ! size t22

i=3, j=1

Blumenhagen et al.

(For W0=10, g s=0.01, etc.)

Living on the edge!!

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

Question:

Unnaturally light scalars?

Loop induced heavy masses

Without SUSY

With SUSY Übernaturalness

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?

Cosmological Inflation

Kähler Moduli Inflation (Blow-up)

volume τn

V Small field inflation (r<<<1) No fine-tuning!! 0.960<n<0.967 Loop corrections??

~

V

Fibre Inflatons Burgess, Cicoli, FQ

Ne

ns

ns

r r

Observable gravity waves !

(can be ruled out by Planck if they observe them and CMBpol… if they do not observe them)

Stringy Curvaton Scenario

Curvaton Mass:

Non-Gaussianities Examples

Model Building

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 Blumenhagen et al.

Donagi, Wijnholt; Vafa, Heckman, …

Aldazabal et al.

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!!!)

Toric Singularities

Einstein-Sasaki

T3 Fibration Over rational polyhedral cone

Toric Diagram

D3-branes

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

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

Anomaly/tadpole cancelation

Hypercharge (ni≠nj)

3 Families!

D7s:Franco-Uranga

Standard Models LR-Symmetric Models

Pati-Salam Models Trinification Models

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)

Generic Features

•  Aproximate Flavour Symmetries

•  Hyperweak Interactions (SM fields charged under D7 gauge interactions g2=1/V2/3 <<<1, CDF?)

Burgess et al. 2008

Conlon, Maharana, FQ

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= Σi 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

Minimal del Pezzo?

•  dP0 no hierarchy of masses (unless non-commutative), no CKM

•  dP1, dP2 no CKM or PMNS, no control of kinetic terms (FCNC?).

•  dP3 flavor diagonal kinetic terms and realistic CKM, PMNS matrices.

‘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

Quarks+leptons

• CKM Matrix

• PMNS Matrix

• 14 Parameters vs 21 Observables

Gauge Coupling Unification

String scale value of all couplings given by dilaton so unification.

Standard GUT scale unification or ‘intermediate’ scale Ms>1012 GeV

Need moduli stabilisation to fix scales.. (Large volume scenarios?....)

SUSY BREAKING

SUSY Breaking •  Approximate Universality

•  Two cases: FSM≠0 soft terms~m3/2 Ms~10

12 GeV

FSM=0 soft terms <<m3/2

or~m3/2

CAQS, Conlon (Mirror Mediation)

CONCLUSIONS •  Continuous progress on local string

models (TeV warping, TeV gravity, TeV SUSY!?)

•  Several SUSY breaking scenarios (m~m3/2, m3/2

3/2/Mp1/2, m3/2

2/Mp ), (Ms~103 – 1016 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