Presentation on theme: "אוניברסיטת בן - גוריון Ram Brustein Moduli space of effective theories of strings Outer region of moduli space: problems! “central” region: stabilization."— Presentation transcript:
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/ PRD 64 (2001), hep-th/ hep-th/ hep-th/ with S. de Alwis, E. Novak Moduli stabilization, SUSY breaking and Cosmology
HO I IIB IIA HW MS1 HE String Theories and 11D SUGRA HW=11D SUGRA/I 1 MS1=11D SUGRA/S 1 T T S S “S” N=1 (10D) N=2 (10D) “S”
String Moduli Space HO I IIB IIA HW MS1 HE Requirements D=4 N=1 SUSY N=0 CC<(m 3/2 ) 4 SM (will not discuss) Volume/Coupling moduli TS Central region “minimal computability” Outer region perturbative 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 –P ractical C osmological C onstant P roblem –Runaway potentials (not solved by duality)
BPS Brane-instanton SNP’s Euclidean wrapped branes Potential V~e -action Complete under duality From hep-th/
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 point In 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 potential Ansatz Solution No slow-roll for real steep potential realistic steep potential
Central Region Parametrization with D=4, N=1 SUGRA Stabilization by SNP string scale Continuously adjustable parameter SUSY lower scale by FT effects PCCP o.k. after SUSY breaking Our proposal: VADIM: CAN YOU HAVE A CONTINOUSLY ADJUSTABLE PARAMETER THAT IS NOT A MODULUS? ARE 2 AND 3 CONSISTENT OFER: KACHRU ET AL CENTRAL REGION. DISCRETE PARAMETER
Stable SUSY breaking minimum Two Moduli, S (susy breaking direction), T (orthogonal), m 3/2 /M P = ~10 -16
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 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 M S 8 V 6 (M 11 9 V 7 in M). Curvature term multiplied by same factors “Calibrate” using 4D Newton’s const. 8 G N =m p -2 Typical distances are O(m p)
The scale of the potential Numerical examples: NO VOLUME FACTORS!!! Banks
The shape of the potential m p outer region V( M S 6 m p -2 outer region central region zero CC min. & potential infinity intermediate max.
Inflation: constraints & predictions Topological inflation – wall thickness in space Inflation H > 1 > m p H 2 ~1/3 m p 2 m p V( M S 6 m p -2
CMB anisotropies and the string scale For consistency need |V’’|~1/25 Slow-roll parameters Number of efolds The “small” parameter Sufficient inflation Qu. fluct. not too large
1/3 < 25|V’’| < 3 For our model If consistent: 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