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אוניברסיטת בן-גוריון

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

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אוניברסיטת בן-גוריון

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  1. 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 • Outer region of moduli space: problems! • “central” region: • stabilization • interesting cosmology

  2. String Theories and 11D SUGRA S N=2 (10D) IIB T I S IIA “S” HO T HW MS1 “S” HE HW=11D SUGRA/I1 MS1=11D SUGRA/S1 N=1 (10D)

  3. Perturbative theories = phenomenological disaster • SUSY+msless moduli • Gravity = Einstein’s • Cosmology String Moduli Space Central region “minimal computability” IIB I IIA HO String universality ? Outer region perturbative HW MS1 HE • Requirements • D=4 • N=1 SUSY  N=0 • CC<(m 3/2)4 • SM (will not discuss) • Volume/Coupling moduli • T S

  4. Cosmological moduli space

  5. “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)

  6. BPS Brane-instanton SNP’s From hep-th/0002087 Euclidean wrapped branes Potential V~e-action Complete under duality

  7. Outer Region Moduli – chiral superfields of N=1 SUGRA, N=1 SUGRA Steep potentials K=K(S,S*), W=W(S) e.g: K=-ln(S+S*) Pert. Kahler L<0

  8. (ii) Two types: (i) Min?, Max?, Saddle? Outer Region Stabilization ? Extremum:

  9. Case (i) Case (i) is a minimum Case (ii) Case (ii) is a saddle point In general, max or saddle, but never min !

  10. Outer Region Cosmology:Slow-Roll? • Without a potential: 4D, 5D, 10D, 11D : “fast-roll” 5D – same solutions! S-duality T-duality

  11. Ansatz Solution Use to find properties of solutions with real potential With a potential realistic steep potential No slow-roll for real steep potential

  12. Central Region Our proposal: • 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 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

  13. Stable SUSY breaking minimum Two Moduli, S (susy breaking direction), T (orthogonal) , m3/2/MP=e~10-16

  14. (1) (2) (3) (4) (5) (b),(c ),(e) & (2)  (a),(b),(e) & (2,3,4) 

  15. With more work • 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(e) in general masses of T moduli O(1).

  16. Simple example • Reasonable working models, • Additional SUSY preserving L<0 minima!

  17. Scales & Shape of Moduli Potential • The width of the central region In effective 4D theory: kinetic terms multiplied by MS8 V6 (M119 V7 in M). Curvature term multiplied by same factors “Calibrate” using 4D Newton’s const. 8pGN=mp-2 • Typical distances are O(mp)

  18. The scale of the potential NO VOLUME FACTORS!!! Banks Numerical examples:

  19. V(f)/MS6mp-2 outer region outer region 2 -1 central region f/mp -4 -2 0 2 4 The shape of the potential zero CC min. & potential vanishes @ infinity  intermediate max.

  20. V(f)/MS6mp-2 2 -1 f/mp -4 -2 0 2 4 Inflation: constraints & predictions • Topological inflation D • –wall thickness in space (D/d)2 ~ L4 Inflation dH > 1 D> mp H2~1/3 L4/mp2

  21. Slow-roll parameters The “small” parameter Number of efolds CMB anisotropies and the string scale Sufficient inflation Qu. fluct. not too large For consistency need |V’’|~1/25

  22.  1/3 < 25|V’’| < 3  For our model • WMAP If consistent:

  23. 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

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