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The LARGE Volume Scenario: Realisation and Cosmological Implications. M. Cicoli, J. Conlon, FQ, 0708.1873 [hep-th] + to appear J. Conlon, R. Kallosh, A. Linde, FQ, to appear. F. Quevedo, Cambridge. Liverpool, March 2008. Related talks: E. Plauschinn and E. Palti. String Phenomenology. - PowerPoint PPT Presentation
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The LARGE Volume Scenario: Realisation and Cosmological
Implications
M. Cicoli, J. Conlon, FQ, 0708.1873 [hep-th] + to appearJ. Conlon, R. Kallosh, A. Linde, FQ, to appear
F. Quevedo, Cambridge. Liverpool, March 2008.
Related talks: E. Plauschinn and E. Palti
String Phenomenology• Explicit Realistic Models(SU(3)xSU(2)xU(1), 3 families, etc.)
• Model Independent Issues(axions, no-global symmetries,….,SUSY breaking, moduli
stabilisation,…)
• 4D Effective Actions(Explicit form of K, W, f. For N=1 compactifications)
Why LARGE volume?• Effective field theory robust• Phenomenology M2
Planck=M2
string V
V=104 Mstring=MGUT=1017GeV
V=1030 Mstring=1 TeV
V=1015 Mstring=1011 GeV
(Also RS warping !)
MODULI STABILISATION?
Exponentially Large Volumes in IIB
Perturbative vs Non perturbative :
• In general:
• Then:
• Usually V0 dominates but V0=0 (no-scale )
• Dominant term is VJ unless W0<<1 (KKLT)
Exponentially Large Volumes• Perturbative (alpha’) corrections to K • At least two Kähler moduli (h21>h11>1)Example :
BBCQ, CQS (2005)BBCQ, CQS (2005)
String scale: Ms2=M2
Planck/VW0~1-10Ms=1 TeV problematic from 5th force
Exponentially large volumen !!!
as~2π/gs N
UniverseUniverse
D3 BraneD3 Brane
oror
D7 BraneD7 Brane
Standard Model on D7 Branes
• Solve hierarchy problem Mstring = 1011 GeV!
• W0~1 (no fine tuning)
• Kahler potential for chiral matter computedConlon, Cremades, FQ (2006) Conlon, Cremades, FQ (2006)
The Standard Model in the CYThe Standard Model in the CY
Chiral Matter on D7 BranesSoft SUSY Breaking terms
• Universality!Universality!• No extra CP violation!No extra CP violation!• MMii = m = m3/23/2 / log (Mp/m / log (Mp/m3/23/2))• String scale 10String scale 101111 GeV GeV • Solves hierarchy problem!Solves hierarchy problem!
Conlon et al.Conlon et al.
Simplest case λ=1/3
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
• For Nsmall blow-up modes, there are L=h11-Nsmall-1 flat directions at tree-level
• These directions are usually lifted by perturbative effects
L moduli lighter than volume!
String Loop Corrections
Berg-Haack-KorsBerg-Haack-Kors
Berg-Haack-Pajer Berg-Haack-Pajer
Leading order correction for V is alpha’ but string loops relevant to fix other moduli
TauSM
Example 1Example 1Blumenhagen et alBlumenhagen et al
Example 2: K3 Fibrations• K3 Fibration with 2 Kahler moduli [1,1,2,2,6] model
• No LARGE volume
• K3 Fibration with 3 Kahler moduli (one blow- up)
• tau3 small, tau 1 and tau 2 LARGE
V
Volume,
COSMOLOGY
(Inflation, Cosmological moduli problem, etc.)
BRANE - ANTIBRANE INFLATIONBRANE - ANTIBRANE INFLATION
All branes inflate while two approachAll branes inflate while two approach
Inflaton: Open string mode Inflaton: Open string mode (talks by R. Gregory, M. Haack and H. Stoica)(talks by R. Gregory, M. Haack and H. Stoica)
KAHLER MODULI INFLATION
Candidate Inflatons: Closed string modes
Kahler Moduli (size/axion)
Small modulus inflaton
Kähler Moduli Inflation
Calabi-Yau: h2121>>h1111>2
volume τn
V
Conlon-FQ Conlon-FQ
Bond-Kofman-ProkushkinBond-Kofman-Prokushkin
Small field inflationNo fine-tuning!!0.960<n<0.967
Open Questions• Loop effects tend to spoil flatness
• Non tensor perturbations (r=T/S<<<1)?
• Tension phenomenology vs cosmology
Gravitino mass 1 TeV/Gravitino mass >> 1 TeV ??
(string scale 10 11 GeV/ string scale ~ GUT scale)
Low Energy SUSY vs Inflation
• Low scale inflation?
• Runaway before reheating? Conlon, Kallosh, Linde, FQ
Ross et al, …
No Overshooting problem!!!
New Candidate Inflatons
• L=h11-Nsmall-1 `almost’ flat directions are light
• Mass=V-5/3< Volume modulus mass m=V-3/2~H
• Recall η ~ mass2/H Cicoli et al.
After Inflation
Physics of Moduli Fields• Dilaton and Complex
Structure
• Small (heavy) Kahler moduli
• Large (light) Kahler modulus
Moduli masses:
Volume axion m~exp(-V)<<10-33 eV (equality if Mstring=MGUT)!
Summary of couplings
Other Cosmological Implications• Cosmological moduli problem
• Observational implications of light volume modulus?
U,S: trapped at their minimumU,S: trapped at their minimumT: except for volume, heavy and decay fast ! (No T: except for volume, heavy and decay fast ! (No
CMP nor gravitino overproduction)CMP nor gravitino overproduction)Volume: (mass MeV) CMP Volume: (mass MeV) CMP
Gamma rays, e+-e-
J.Conlon, FQJ.Conlon, FQ
DCQR, BKNDCQR, BKN
The 511 keV LineThe 511 keV Line
INTEGRAL/ SPI 511 keV lineINTEGRAL/ SPI 511 keV line
Light Modulus χ: Dark matter?Mass 1MeV, coupling to electrons dominant
511 keV from volume modulus decay? (prediction!)511 keV from volume modulus decay? (prediction!)BUT `almost’ ruled out 2 months ago!!!BUT `almost’ ruled out 2 months ago!!!
Intensity
INTEGRAL
General Picture• Nsmall heavy Kahler moduli (cosmological harmless)
• Volume modulus (CMP + 511 keV line+ predicted monochromatic line!) (see Boyarski et al)
• L=h11-Nsmall-1 lighter moduli (candidate inflatons, CMP, new monochromatic lines!! (observable?))
• CMP (late low energy inflation?)
Conclusions• Non-perturbative effects fix only a fraction of
Kahler moduli (Nsmall)• Alpha’ effects fix volume to exponentially large
values (Both LARGE volume and large warping in the same class of models!?)
• Loop corrections needed to fix the rest of Kahler moduli
• Interesting phenomenology/cosmology• Astrophysics (forest of monochromatic lines?)• Fully realistic model?
Solution of CMP?Thermal Inflation
Lyth+Stewart (1995)Lyth+Stewart (1995)
Number of e-folds
N~10 dilutes moduli