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INCLINED DIMENSIONS Daniel Hernández The Abdus Salam International Center for Theoretical Physics D.H, M. Sher; 1101.5695 Phys. Let. B.

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F UN WITH PHYSICS LORENTZ VIOLATION WARPED EXTRA DIMENSIONS SLANTED BRANE MODEL (and some nice graduate-level physics)

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

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MOST IMPORTANTLY, WHY ISN’T IS HOPELESS?? Spontaneous LV is a generic prediction of Quantum Gravity: Some stringy models, Loop QG. Also connected with CPT Non-invariance. 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! W HY (true) LORENTZ VIOLATION?

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

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BOUNDS ON LORENTZ VIOLATION S. Liberati, L. Maccione; 0906.0681 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) …….

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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

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TOTALLY UNRELATED A PRIORI: RANDALL-SUNDRUM

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

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

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

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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.

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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!

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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

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

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

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

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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

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KEY POINT: HIERARCHY ACHIEVED BETWEEN PLANCK MASS AND EW SCALE

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

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

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

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THE TILTED METRIC Hubble parameter Non intersecting branes

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

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

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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!

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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

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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

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CMB BOUNDS Temperature of last scatteringBinding energy of hydrogen

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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

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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

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

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

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GENERAL SOLUTION General solution for k

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

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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.

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