1. Extra Dimensions of Space-Time String theory suffers conformal anomaly that makes theory inconsistent --> get rid of it Conformal anomaly ~ (D-26) for a bosonic string ~ (D-10) for a fermionic string String theory suffers conformal anomaly that makes theory inconsistent --> get rid of it Conformal anomaly ~ (D-26) for a bosonic string ~ (D-10) for a fermionic string Is it possible that we actually leave in D > 4? Do we have experimental evidence for D=4, D> 4? Is it possible that we actually leave in D > 4? Do we have experimental evidence for D=4, D> 4? Motivation:

2. Why don’t we see extra dimensions

3. Kaluza-Klein Approach Pseudo-Euclidean space Minkowski space compact space Metrics Fields K-K modes Eigenfunctions of Laplace operator on internal space K d Radius of the compact space Masses Couplings

4. Multidimensional Gravity Action K-K Expansion Newton constant Plank Mass Reduction formula

5. Low Scale Gravity Modified Newton potential 10

6. Brane World Compact DimensionsNon-compact dimensions Kink soliton Energy density brane SM New D4-brane Bulk Localization on the brane R (Potential well) Space-time of Type I superstring

7. The ADD Model SM graviton metric K-K gravitons Interactions with the fields on the brane The # of KK gravitons with masses Emission rate

8. Particle content of ADD model 4-dimensional picture 1 massless graviton (spin 2) + matter KK tower of massive gravitons (spin 2) (d-1) KK spin 1 decoupling fields KK tower of real scalar decoupling fields KK tower of scalar fields (zero mode – radion) (4+d)-dimensional picture: (4+d)-dimensional massless graviton + matter The SM fields are localized on the brane, while gravitons propagate in the bulk The “gravitational” coupling is

9. HEP Phenomenology New phenomena: graviton emission & virtual graviton exchange KK states production bg LHC

10. HEP Phenomenology II Virtual graviton exchange Spin=2 Angular distribution SM q q -

11. Randall-Sandrum Models Plank TeV D4-brane Bulk Metric warp factor Positive tension Negative tension Matter Perturbed Metric gravitonradion

12. Randall-Sandrum Model cont’d Hierarchy Problem ! Brane 1 Massless graviton massive K-K gravitons massless radion Brane 2 Wrap factor Massless graviton massive K-K gravitons massless radion

13. HEP Phenomenology The first KK graviton mode M ~ 1 TeV Drell-Yan process Excess in dijet process TevatronLHC Exclusion plots for resonance production Excluded D-Y Dj Run I Run II D-Y

14. HEP Phenomenology II The x-section of D-Y production Tevatron (M ~ 700 GeV)LHC (M ~ 1500 GeV) First KK modeFirst and subsequent KK modes

15. HEP Phenomenology III LHC Angular dependence LHC

16. ED Conclusion ADD Model The M EW /M PL hierarchy is replaced by For M small enough it can be checked at modern and future colliders For d=2 cosmological bounds on M are high (> 100 TeV), but for d>2 are mild Preictions of modification of the Newton’s law may be checked RS Model The M EW /M PL hierarchy is solved without new hierarchy A large part of parameter space will be studied in future collider experiments With the mechanism of radion stabilization the model is viable Cosmological scenarios are consistent (except the cosmological constant problem)

17. What comes beyond the Standard Model ?