אוניברסיטת בן-גוריון
DESCRIPTION
Ram Brustein. אוניברסיטת בן-גוריון. Moduli stabilization, SUSY breaking and Cosmology. PRL 87 (2001), hep-th/0106174 PRD 64 (2001), hep-th/0002087 hep-th/0205042 hep-th/0212344 with S. de Alwis, E. Novak. Moduli space of effective theories of strings - PowerPoint PPT PresentationTRANSCRIPT
אוניברסיטת בן-גוריון
Ram Brustein
Moduli space of effective theories of strings Outer region of moduli space: problems!
“central” region: stabilization interesting cosmology
PRL 87 (2001), hep-th/0106174PRD 64 (2001), hep-th/0002087
hep-th/0205042hep-th/0212344
with S. de Alwis, E. Novak
Moduli stabilization, SUSY breaking and Cosmology
HO
IIIB
IIA
HWMS1
HE
String Theories and 11D SUGRA
HW=11D SUGRA/I1
MS1=11D SUGRA/S1
T
T
S
S
“S”
N=1 (10D)
N=2 (10D)
“S”
String Moduli Space
HO
IIIB
IIA
HWMS1 HE
Requirements•D=4•N=1 SUSY N=0•CC<(m 3/2)4
•SM (will not discuss)•Volume/Coupling moduli T S
Central region“minimal computability”
Outer regionperturbative
Perturbative theories = phenomenological disaster
•SUSY+msless moduli
•Gravity = Einstein’s
•Cosmology
String universality ?
Cosmological moduli space
“Lifting Moduli”• Perturbative
– Compactifications– Brane Worlds
• Non-Perturbative– SNP = Brane instantons– Field-Theoretic, e.g., gaugino-condensation
• Generic Problems
– Practical Cosmological Constant Problem
– Runaway potentials (not solved by duality)
BPS Brane-instanton SNP’s
Euclidean wrapped branesPotential V~e-action
Complete under duality
From hep-th/0002087
Outer RegionModuli – chiral superfields of N=1 SUGRA,
K=K(S,S*), W=W(S)
N=1 SUGRASteep potentials
e.g:K=-ln(S+S*)Pert. Kahler
Extremum:
Min?, Max?, Saddle?
(ii)Two types:
(i)
Outer Region Stabilization ?
Case (i)
Case (i) is a minimum
Case (ii)
Case (ii) is a saddle pointIn general, max or saddle, but never min !
Outer Region Cosmology:Slow-Roll?
S-duality
5D – same solutions!
T-duality
•Without a potential: 4D, 5D, 10D, 11D : “fast-roll”
•With a potential Use to find properties of solutions with real potentialAnsatz
Solution
No slow-roll for real steep potential
realistic steep potential
Central Region
• Parametrization with D=4, N=1 SUGRA
• Stabilization by SNP effects @ string scale
• Continuously adjustable parameter
• SUSY breaking @ lower scale by FT effects
• PCCP o.k. after SUSY breaking
Our proposal:
VADIM: CAN YOU HAVE A CONTINOUSLYADJUSTABLE PARAMETER THAT IS NOT A MODULUS? ARE 2 AND 3 CONSISTENTOFER: KACHRU ET AL CENTRAL REGION.DISCRETE PARAMETER
Stable SUSY breaking minimum
Two Moduli, S (susy breaking direction), T (orthogonal) , m3/2/MP=~10-16
(a),(b),(e) & (2,3,4)
(b),(c ),(e) & (2)
(2)
(3)
(1)
(4)
(5)
•Higher derivatives in S (> 3) and T (> 1), & mixed derivatives of order > 2 generically O(1).
•In SUSY limit, in T direction, V is steep, all derivatives > 2 generically O(1) @ min. In S direction, potential is very flat around min.
•Masses of SUSY breaking S moduli o( in general masses of T moduli O(1).
With more work
Simple example
Reasonable working models, Additional SUSY preserving <0 minima!
Scales & Shape of Moduli Potential• The width of the central region
In effective 4D theory: kinetic terms multiplied by MS
8 V6 (M119 V7 in M).
Curvature term multiplied by same factors“Calibrate” using 4D Newton’s const. 8GN=mp
-2
Typical distances are O(mp)
22421
pp mRgmxd
• The scale of the potential
)/(
)(
4214
42214
p
p
mVxd
Vmxd
4263 / pSS mMVMW
Numerical examples:
4/34/3
25/116106.8 gGeV YM
I
2/36/16
4/1
25/116 )4(106.7
VMGeV GUTHWYM
NO VOLUME FACTORS!!!Banks
• The shape of the potential
mp
outer region
-4 -2 0 2 4
2
-1
V(MS6mp
-2
outer regioncentral region
zero CC min. & potential vanishes @ infinity intermediate max.
Inflation: constraints & predictions
• Topological inflation
– wall thickness in spaceInflation H > 1 > mp H2~1/3 mp
2
mp-4 -2 0 2 4
2
-1
V(MS6mp
-2
|)(''|252/|)(''|105.6 max4/1
max162 VExpVGeV
CMB anisotropies and the string scale
For consistency need |V’’|~1/25
dNend
pmend )(
121),(
)(''~,2~ max2
max4
2
Vmp
|(''|
22
max)
2
V
mp
Slow-roll parameters
Number of efolds
The “small” parameter
Sufficient inflation 2max )/(120 pinit mExp
6/1)('' max2max VHinit Qu. fluct. not too large
0
)1|)(''|25(08.92. max
r
VnS CMB
CMBCMBS
r
n
7.13
241
1/3 < 25|V’’| < 3 0
97.76.
r
nS
0)(''
0~)/'(
max
2
V
VV
CMB
CMBFor our model
If consistent:
)1(6/11
3/1
10
17 325
4
2/1
)(107.1 S
S
nn
P
S eGeVM
WMAP
Summary and Conclusions• Stabilization and SUSY breaking
– Outer regions = trouble– Central region: need new ideas and techniques– Prediction: “light” moduli
• Consistent cosmology: – Outer regions = trouble– Central region:
– scaling arguments– Curvature of potential needs to be “smallish”
– Predictions for CMB