INCLINED DIMENSIONS
description
Transcript of INCLINED DIMENSIONS
![Page 1: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/1.jpg)
INCLINED DIMENSIONS
Daniel Hernández
The Abdus Salam International Center for Theoretical Physics
D.H, M. Sher; 1101.5695
Phys. Let. B.
![Page 2: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/2.jpg)
FUN WITH PHYSICS
LORENTZ VIOLATION WARPED EXTRA DIMENSIONS
SLANTED BRANE MODEL
(and some nice graduate-level physics)
![Page 3: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/3.jpg)
WHAT 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
![Page 4: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/4.jpg)
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!
WHY (true) LORENTZ VIOLATION?
![Page 5: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/5.jpg)
THE SM EXTENSION
Idea: Parametrize Lorentz Violation through effective operators
EFECTIVE FIELD THEORY
………………
Changed vev of the Higgs
Colladay, Kostelecky
![Page 6: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/6.jpg)
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)
• …….
![Page 7: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/7.jpg)
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
![Page 8: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/8.jpg)
TOTALLY UNRELATED A PRIORI: RANDALL-SUNDRUM
![Page 9: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/9.jpg)
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
![Page 10: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/10.jpg)
A VERY STUPID LAGRANGIAN (cont.)
What about a lambda(phi)^4 term???
NO CHANGE
Think now of the Higgs and the possibilities?? Mmmmmm
![Page 11: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/11.jpg)
A VERY STUPID LAGRANGIAN (cont.)
Higgs mass depends on the scale factor???
FRW metric
![Page 12: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/12.jpg)
WHY IT IS STUPIDAlways 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.
![Page 13: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/13.jpg)
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!
![Page 14: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/14.jpg)
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
![Page 15: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/15.jpg)
RANDALL-SUNDRUM’S IDEA
WORKS LIKE MAGIC AS WESHALL SEE
Lisa Randall performing her spell
![Page 16: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/16.jpg)
RANDALL-SUNDRUM’S IDEA(explicitly)
Start in 5D Anti de Sitter
We know this fulfills the 5D Einstein equations With negative cosmological constant
![Page 17: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/17.jpg)
RANDALL-SUNDRUM’S IDEA(explicitly)
Put 4D branes, restrict the domain
Higgs on the brane Induced by
![Page 18: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/18.jpg)
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
![Page 19: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/19.jpg)
KEY POINT: HIERARCHY ACHIEVED BETWEEN PLANCK MASS AND EW SCALE
![Page 20: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/20.jpg)
PUTTING MATTER
T. Gherghetta, A. Pomarol; hep-ph/0003129
The procedure is simple and well known
Kaluza Klein decomposition
![Page 21: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/21.jpg)
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
![Page 22: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/22.jpg)
‘So, what if we tilt the branes?’
‘That would immediately give Lorentz violation’
![Page 23: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/23.jpg)
THE TILTED METRIC
Hubble parameter
Non intersecting branes
![Page 24: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/24.jpg)
THE TILTED METRIC
Is it a solution to the Einstein eqs??
Same as in parallel brane scenario at this order
And flat visible brane!
![Page 25: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/25.jpg)
Induces a vev for the Z boson and modifiesthe Higgs vevOrder a^2. Not measurable.
HIGGS NORMALIZATION
![Page 26: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/26.jpg)
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!
![Page 27: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/27.jpg)
VARIABLE HIGGS MASS
The main effect is that it alters fermion masses. For fermionson the branes, the Yukawa couplings are not altered by the tiltand the masses are simply scaled by the warp factor
Search for cosmic variance of the masses of elementary particles
![Page 28: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/28.jpg)
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
![Page 29: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/29.jpg)
CMB BOUNDS
Temperature of last scattering Binding energy of hydrogen
![Page 30: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/30.jpg)
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
![Page 31: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/31.jpg)
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
![Page 32: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/32.jpg)
GENERAL SOLUTION
Consider the Einstein equation
The ansatz
Gives a diagonal Einstein tensor (to no surprise)
![Page 33: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/33.jpg)
GENERAL SOLUTION
Second order in a
Two more equations appearing from the Einstein eqs
![Page 34: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/34.jpg)
GENERAL SOLUTION
General solution for k
![Page 35: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/35.jpg)
This corresponds to Randall Sundrum
This is the full analytical metric for which the tilted metric is the first order approximation
For example:
![Page 36: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/36.jpg)
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.
![Page 37: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/37.jpg)
![Page 38: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/38.jpg)
![Page 39: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/39.jpg)
![Page 40: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/40.jpg)
![Page 41: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/41.jpg)
![Page 42: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/42.jpg)
![Page 43: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/43.jpg)
![Page 44: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/44.jpg)
![Page 45: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/45.jpg)
![Page 46: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/46.jpg)
![Page 47: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/47.jpg)
![Page 48: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/48.jpg)
![Page 49: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/49.jpg)
![Page 50: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/50.jpg)
![Page 51: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/51.jpg)
![Page 52: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/52.jpg)
![Page 53: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/53.jpg)
![Page 54: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/54.jpg)
![Page 55: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/55.jpg)
![Page 56: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/56.jpg)
![Page 57: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/57.jpg)
![Page 58: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/58.jpg)
![Page 59: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/59.jpg)
![Page 60: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/60.jpg)
![Page 61: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/61.jpg)
![Page 62: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/62.jpg)
![Page 63: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/63.jpg)
![Page 64: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/64.jpg)
![Page 65: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/65.jpg)
![Page 66: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/66.jpg)
![Page 67: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/67.jpg)
![Page 68: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/68.jpg)
![Page 69: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/69.jpg)
![Page 70: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/70.jpg)
![Page 71: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/71.jpg)
![Page 72: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/72.jpg)
![Page 73: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/73.jpg)
![Page 74: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/74.jpg)
![Page 75: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/75.jpg)
![Page 76: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/76.jpg)
![Page 77: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/77.jpg)
![Page 78: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/78.jpg)
![Page 79: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/79.jpg)
![Page 80: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/80.jpg)
![Page 81: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/81.jpg)
![Page 82: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/82.jpg)
![Page 83: INCLINED DIMENSIONS](https://reader036.fdocuments.in/reader036/viewer/2022062310/568164bf550346895dd6cf22/html5/thumbnails/83.jpg)