Moduli stabilization SUSY breaking and Cosmology Ram Brustein

Moduli stabilization, SUSY breaking and Cosmology Ram Brustein גוריון - אוניברסיטת בן 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

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

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

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 From hep-th/0002087 Euclidean wrapped branes Potential V~e-action Complete under duality

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

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

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

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

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

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.

Stable SUSY breaking minimum Two Moduli, S (susy breaking direction), T (orthogonal) , m 3/2/MP=e~10 -16

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).

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

Scales & Shape of Moduli Potential • The width of the central region In effective 4 D theory: kinetic terms multiplied by MS 8 V 6 (M 119 V 7 in M). Curvature term multiplied by same factors “Calibrate” using 4 D Newton’s const. 8 p. GN=mp-2 Typical distances are O(mp)

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

• The shape of the potential V(f)/MS 6 mp-2 outer region -4 outer region 2 central region -2 0 2 4 f/mp -1 zero CC min. & potential vanishes @ infinity intermediate max.

Inflation: constraints & predictions • Topological inflation V(f)/MS 6 mp-2 2 -4 -2 0 -1 2 D 4 f/mp d – wall thickness in space (D/d)2 ~ L 4 Inflation d. H > 1 D> mp H 2~1/3 L 4/mp 2

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

For our model 1/3 < 25|V’’| < 3 If consistent: ü 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