1 / 83

INCLINED DIMENSIONS

INCLINED DIMENSIONS. Daniel Hernández The Abdus Salam International Center for Theoretical Physics. D.H, M. Sher ; 1101.5695. Phys. Let. B. . F UN WITH PHYSICS. WARPED EXTRA DIMENSIONS. LORENTZ VIOLATION. SLANTED BRANE MODEL. (and some nice graduate-level physics).

maree
Download Presentation

INCLINED DIMENSIONS

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. INCLINED DIMENSIONS Daniel Hernández TheAbdusSalam International Center forTheoreticalPhysics D.H, M. Sher; 1101.5695 Phys. Let. B.

  2. FUN WITH PHYSICS WARPED EXTRA DIMENSIONS LORENTZ VIOLATION SLANTED BRANE MODEL (and some nice graduate-level physics)

  3. WHAT LORENTZ VIOLATION? For instance Particle physics doesn’t respect Lorentz symmetry Inhomogeneous, anisotropic, space-time LORENTZ AS A GAUGE SYMMETRY IS VIOLATED NOTHING IS VIOLATED REALLY

  4. WHY (true) LORENTZ VIOLATION? Spontaneous LV is a generic prediction of Quantum Gravity: Some stringy models, Loop QG. Also connected with CPT Non-invariance. MOST IMPORTANTLY, WHY ISN’T IS HOPELESS?? Great improvement in experimental techniques over the last 10-15 years making it possible to test LV effects even if suppressed by the Planck scale!

  5. THE SM EXTENSION EFECTIVE FIELD THEORY Idea: Parametrize Lorentz Violation through effective operators ……………… Changed vev of the Higgs Colladay, Kostelecky

  6. BOUNDS ON LORENTZ VIOLATION Lots of papers, lots of ways, sometimes very ingenious to put bounds • Photon time of flight • Vacuum Birrefringence • Threshold reactions (Very spectacular effects like photon decay) • ……. S. Liberati, L. Maccione; 0906.0681

  7. I won’t speak about True Lorentz Violation… However, I will argue that the SM Extension is also useful to describe the field theory of non maximally symmetric spaces

  8. TOTALLY UNRELATED A PRIORI: RANDALL-SUNDRUM

  9. A VERY STUPID LAGRANGIAN Free field in a perfectly Minkowski BG Explicitly: Wave function normalization So, what is the PHYSICAL mass of this scalar field??

  10. A VERY STUPID LAGRANGIAN (cont.) What about a lambda(phi)^4 term??? NO CHANGE Think now of the Higgs and the possibilities?? Mmmmmm

  11. A VERY STUPID LAGRANGIAN (cont.) FRW metric Higgs mass depends on the scale factor???

  12. WHY IT IS STUPID Always consider the FULL Lagrangian These two need be the same! So, nothing wrong with changing variables, but beware of interpretation. Specially when metric perturbations are important.

  13. STUPID IS INTERESTING (rarely) Nonetheless, if we could have such a Higgs, it would be very cool, right? A time evolving Higgs! Or thinking general. A vev for the Higgs that depends on the metric!

  14. WHAT ONE WOULD NEED Write the full Lagrangian… Absorb the conformal factor in the fields of the matter Lagrangian Hope that the remaining Lagrangian «accepts» the new metric

  15. RANDALL-SUNDRUM’S IDEA WORKS LIKE MAGIC AS WE SHALL SEE Lisa Randall performing her spell

  16. RANDALL-SUNDRUM’S IDEA(explicitly) Start in 5D Anti de Sitter We know this fulfills the 5D Einstein equations With negative cosmological constant

  17. RANDALL-SUNDRUM’S IDEA(explicitly) Put 4D branes, restrict the domain Higgs on the brane Induced by

  18. RANDALL-SUNDRUM’S IDEA(explicitly) Normalize Higgs field Watch the magic The metrics here are not simply Anti de Sitter and Minkowski but perturbed Anti de Sitter and Minkowski

  19. KEY POINT: HIERARCHY ACHIEVED BETWEEN PLANCK MASS AND EW SCALE

  20. PUTTING MATTER The procedure is simple and well known Kaluza Klein decomposition T. Gherghetta, A. Pomarol; hep-ph/0003129

  21. PUTTING FERMIONS Substitute in the 5D Lagrangian, integrate for the extradimensional coordinate The Flavour puzzle encoded in the Yukawas is transferred to the c_i T. Gherghetta, A. Pomarol; hep-ph/0003129

  22. ‘So, what if we tilt the branes?’ ‘That would immediately give Lorentz violation’

  23. THE TILTED METRIC Non intersecting branes Hubble parameter

  24. THE TILTED METRIC Is it a solution to the Einstein eqs?? And flat visible brane! Same as in parallel brane scenario at this order

  25. HIGGS NORMALIZATION Induces a vev for the Z boson and modifies the Higgs vev Order a^2. Not measurable.

  26. PLANCK MASS If one wants to absorb the conformal factor in the metric one needs to follow the procedure outlined for the RS metric!! Won’t explore this further!

  27. VARIABLE HIGGS MASS The main effect is that it alters fermion masses. For fermions on the branes, the Yukawa couplings are not altered by the tilt and the masses are simply scaled by the warp factor Search for cosmic variance of the masses of elementary particles

  28. TRIPLE ALPHA PROCESS Lifetime of order 10^-16 secs Resonance of 12C state enhances reaction rate! Energy of the resonance dependent on the nucleon mass

  29. CMB BOUNDS Temperature of last scattering Binding energy of hydrogen

  30. BEST BOUND OF ALL: AMMONIA Ammonia clouds in the path of light coming from distant quasars Inversion transition very sensitive to the proton to electron mass ratio Comparing with the rotational spectra

  31. FERMIONS IN THE BULK The above is not valid in a direct manner, essentially because one needs to solve again for the wavefunction. Remember the Kaluza-Klein procedure. However, very crude estimates point that the previous bounds are valid (maybe even ) improved for fermions in the bulk

  32. GENERAL SOLUTION Consider the Einstein equation The ansatz Gives a diagonal Einstein tensor (to no surprise)

  33. GENERAL SOLUTION Second order in a Two more equations appearing from the Einstein eqs

  34. GENERAL SOLUTION General solution for k

  35. This corresponds to Randall Sundrum This is the full analytical metric for which the tilted metric is the first order approximation For example:

  36. CONCLUSIONS • An scenario with tilted branes is plausible, at least at the classical level. • Two types of modifications in the Lagrangian. One can be interpreted in the context the Lorentz violating Standard Model extension. The other is a typical sidereal classical field which yields masses for the SM fields that vary with space • Moreover, generalizing this, a new background solution for the Einstein equations has been found that reduces both to the RS solution and to the tilted metric in the proper limits. • Bounds on the «tilt parameter» are very stringent as expected from any Lorentz violating parameter. However, since it comes from the metric this parameter is stable.

More Related