1 / 23

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

opa
Download Presentation

אוניברסיטת בן-גוריון

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related