Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Vanishing Dimensions
        Dejan Stojkovic
          SUNY at Buffalo




     Balkan Summer Institute
   Djer dap, Aug 1...
Based on:
Detecting Vanishing Dimensions Via Primordial Gravitational Wave Astronomy
J. Mureika, D. Stojkovic,
Phys. Rev. ...
Motivation
•
    Modern physics faces problems that need prompt attention

•
     SM hierarchy, cosmological constant, dar...
Click to edit Master text styles
     Second level
              ●
                Third level
                           ...
The current wisdom

•
    Let’s make the things more complicated

•
    Introduce extra dimensions, new particles, new str...
Proposal
•


    §
        Number of dim depends on scale which we are probing

          •
              Short scales (L ...
Example
•



    An example of a structure which is 1d on short scales
    while it appears effectively 2d on large scales...
Ordered Lattice
•


Ordered Lattice. This structure is

•
    1d on scales 0 < L < L1,

•
    2d on scales L1 < L < L2

•
...
Graphene
     Nature already builds these
     structures

L2


                                   L1




L3
Benefits?


What do we gain by having less dimensions at high energies?




                                              ...
The hierarchy problem

The standard model Lagrangian




•
    Radiative corrections to the Higgs mass:




•
    If SM is...
The hierarchy problem


•
    Gauge boson corrections to the Higgs mass:
The hierarchy problem

    If   3d → 2d crossover happens at 1 TeV
         2d → 1d crossover happens at 10-100 TeV




•
...
What about gravity?

In 2+1 dim any solution of the vacuum Einstein's eq. is locally flat




•
    no local gravitational...
No Black Holes in 2+1 dim

In 2+1 dim any solution of the vacuum Einstein's eq. is locally flat



No real singularities –...
Gravity stops being GR?

In 1+1 dim




Unless augmented by some scalar field




Fully integrable and quantizable
Benefits?


What do we gain by having more dimensions at large scales?




                                               ...
Our Universe may be 4+1 dim on large scales
 •
     Many 3d sheets comprise 4d space
 •
     Stars and galaxies are on 3d ...
Cosmological constant
In 4+1 dim, 3d homogeneous and isotropic solution




Vacuum equations GAB = 0, for a 3d observer at...
Other large scale puzzles
   •
       Bulk flow
   •
       “Axes of Evil”
   •
       Lack of CMB power on large scales

...
How to describe this evolving background?

gμ - metric on a higher dimensional manifold
  ν
γab - metric on a sub-manifold...
How to describe this evolving background?

I. R. Klebanov and L. Susskind, Nucl.Phys. B 309, 175 (1988)


   Take a string...
Result
•


    •
        Such a string builds this structure:




    •
        total length of the string grows as N
    ...
How do particles propagate on this background?
                      B

                              Between any two poin...
Geometry of the lattice




“Natural” Lattice                Stack of branes             Random Lattice


•
    In all cas...
Geometry of the lattice




                   Random Lattice


Avoids preferred direction in space

Avoids systematic vio...
Lorentz symmetry violation
    Lorentz invariance is restored on average on large distances

     However, small fluctuati...
Gamma rays and Fermi satellite




GRB           Space-time foam

                                          Earth
Fermi ob...
Fermi result and vanishing dimensions


• Caveats:

i.   Only one event observed
ii. Physics of the source poorly understo...
Fermi result and vanishing dimensions


• Fundamental objection:
Discrete structures don’t automatically imply
Lorentz sym...
Regular vs. random lattice
F. Dowker, J. Henson, R. Sorkin, gr-qc/0311055




              Regular lattice in two differe...
Effective speed of light
                                                                              B


•   To propagat...
LIV and vanishing dimensions

We can’t take limits on LIV face value (E* ≥
MPl )
We simply do not understand how particles...
String theory solutions
 C. Callan, J. Maldacena, Nucl.Phys. B513, 198 (1998)
                       N. Constable, R. Myer...
Experimental evidence?

Experimental evidence for vanishing dimensions may already exists.


  Alignment of high energy se...
Circle:            Ellipse:               Line:
3d event           Somewhat planar        Pure 2d event
λ=0               ...
Experimental evidence?

     •
         Most of the aligned events originate just above the chamber
     •
         Thus, ...
Possible LHC signature

If the alignment in cosmic rays at ECOM > 4 TeV is not a fluke




      LHC might observe similar...
LHC signature

          If the fundamental high energy physics is 2d , the following
          must be true regardless of...
3d momentum conservation
            If λde Broglie < L3
            particle propagates locally in 2d, rather than 3d

  ...
2d scattering
For scattering to be 2d , wavelength of the mediator must be < L3



                                       ...
2d vs 3d scattering

      Cross-section in 2d is a line (not a disk as in 3d)


                                        3...
2d vs 3d scattering
Coulomb Potential:
 3d                  →   α is dimensionless
 2d                  →   α = L-1



 3d...
2d vs 3d scattering
 Drell-Yan cross section will drop as 1/E3 instead of 1/E2
once the 3d → 2d crossover energy is surpas...
Planar multijet events

            In 2 → 3 scattering with Q2 > Λ32 , all the virtual
            particles (propagators...
Planar multijet events
•
    Local plane absorbs the initial p┴ momentum
•
    Planar scattering happens in c.o.m. frame
•...
Planar multijet events

      3d scattering                         2d scattering




Need 4-jets for acoplanar events in ...
Elliptic Jets
•
    If the lattice orientation is preserved over distances Λ-1QCD
    individual jets at very high energy ...
Lower dim cosmology
•
    FRW metric in 2+1 dim is:




•
    Equations:




•
    Radiation dominated universe:




•
   ...
Lower dim cosmology

•
    FRW metric in 1+1 dim is:




•
    But 1-kx2 can be absorbed into the definition of x




•
  ...
Ambiguities


•
    No reason to require good Newtonian limit in 2+1 dim:




           valid equations                  ...
Gravity waves signature
In 2+1 dim any solution of the vacuum Einstein's eq. is locally flat




•
    No local gravitatio...
Gravity waves signature
The characteristic frequency of gravitational waves produced at some
time t in the past is redshif...
Gravity waves signature
LISA should be able to see a cut-off in GW frequency




                     LISA’s sensitivity
Conclusions

•
    Fundamental problems have accumulated
•
    Current ideas do not work
•
    Time for radically new idea...
THANK YOU
D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology
Upcoming SlideShare
Loading in …5
×

of

D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 1 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 2 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 3 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 4 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 5 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 6 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 7 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 8 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 9 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 10 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 11 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 12 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 13 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 14 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 15 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 16 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 17 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 18 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 19 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 20 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 21 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 22 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 23 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 24 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 25 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 26 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 27 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 28 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 29 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 30 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 31 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 32 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 33 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 34 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 35 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 36 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 37 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 38 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 39 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 40 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 41 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 42 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 43 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 44 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 45 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 46 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 47 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 48 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 49 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 50 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 51 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 52 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 53 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 54 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 55 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 56 D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology Slide 57
Upcoming SlideShare
Phenomenology
Next
Download to read offline and view in fullscreen.

1 Like

Share

Download to read offline

D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology

Download to read offline

The SEENET-MTP Workshop JW2011
Scientific and Human Legacy of Julius Wess
27-28 August 2011, Donji Milanovac, Serbia

Related Books

Free with a 30 day trial from Scribd

See all

Related Audiobooks

Free with a 30 day trial from Scribd

See all

D. Stojkovic - Vanishing Dimensions: Theory and Phenomenology

  1. 1. Vanishing Dimensions Dejan Stojkovic SUNY at Buffalo Balkan Summer Institute Djer dap, Aug 19 – Sep 1,
  2. 2. Based on: Detecting Vanishing Dimensions Via Primordial Gravitational Wave Astronomy J. Mureika, D. Stojkovic, Phys. Rev. Lett. 106, 101101 (2011). Searching for the Layered Structure of Space at the LHC. L. Anchordoqui, D. Dai, H. Goldberg, G. Landsberg, G. Shaughnessy, D. Stojkovic, T. Weiler, Phys. Rev. D83, 114046 (2011) Vanishing Dimensions and Planar Events at the LHC. L. Anchordoqui, D. Dai, M. Fairbairn, G. Landsberg, D. Stojkovic, e-Print: arXiv:1003.5914 [hep-ph]
  3. 3. Motivation • Modern physics faces problems that need prompt attention • SM hierarchy, cosmological constant, dark matter, initial conditions in cosmology, the black hole information loss problem, quantizing gravity… Many ideas have been put forward, but we are still far from satisfactory solutions It is very difficult to imagine future model building without resolving these issues first!
  4. 4. Click to edit Master text styles Second level ● Third level Outline ● Fourth level ● Fifth level • Brief overview • Dimensionality of space-time • Extra dimensions • Evolving dimensions: Our universe is lower dim on short scales and higher dim on large scales! • Motivation for this proposal • Possible evidence Potential problems Experimental signature
  5. 5. The current wisdom • Let’s make the things more complicated • Introduce extra dimensions, new particles, new structures… • And hope that the problems will miraculously disappear
  6. 6. Proposal • § Number of dim depends on scale which we are probing • Short scales (L < TeV-1) space is lower dimensional • Medium scales (TeV-1 < L < Gpc) space is 3-dim • Large scales (L > Gpc) space is higher dimensional
  7. 7. Example • An example of a structure which is 1d on short scales while it appears effectively 2d on large scales. Credit: G. Starkman
  8. 8. Ordered Lattice • Ordered Lattice. This structure is • 1d on scales 0 < L < L1, • 2d on scales L1 < L < L2 • 3d on scales L2 < L < L3 • …………………..
  9. 9. Graphene Nature already builds these structures L2 L1 L3
  10. 10. Benefits? What do we gain by having less dimensions at high energies? P(r)=? ε(r)=? M(r) =?
  11. 11. The hierarchy problem The standard model Lagrangian • Radiative corrections to the Higgs mass: • If SM is valid all the way to MPl a rather fine-tuned cancellation must take place (about 1 part in 1017)
  12. 12. The hierarchy problem • Gauge boson corrections to the Higgs mass:
  13. 13. The hierarchy problem If 3d → 2d crossover happens at 1 TeV 2d → 1d crossover happens at 10-100 TeV • The hierarchy problem disappears! • No need for new physics – just The Standard Model.
  14. 14. What about gravity? In 2+1 dim any solution of the vacuum Einstein's eq. is locally flat • no local gravitational degrees of freedom • number of degrees of freedom in finite • problem of non-renormalizability disappears
  15. 15. No Black Holes in 2+1 dim In 2+1 dim any solution of the vacuum Einstein's eq. is locally flat No real singularities – NO BLACK HOLES (unless we add negative cosmological constant – BZT black hole) As 3d BH evaporates, it becomes 2d, where it stops being a BH NO INFORMATION LOSS PARADOX
  16. 16. Gravity stops being GR? In 1+1 dim Unless augmented by some scalar field Fully integrable and quantizable
  17. 17. Benefits? What do we gain by having more dimensions at large scales? P(r)=? ε(r)=? M(r) =?
  18. 18. Our Universe may be 4+1 dim on large scales • Many 3d sheets comprise 4d space • Stars and galaxies are on 3d sheets • Universe becomes 4d on scales comparable to the horizon radius horizon size
  19. 19. Cosmological constant In 4+1 dim, 3d homogeneous and isotropic solution Vacuum equations GAB = 0, for a 3d observer at ψ = const, look like where Tμ is induced matter with p = - ρ, ν ρ = Λ/(8πG)
  20. 20. Other large scale puzzles • Bulk flow • “Axes of Evil” • Lack of CMB power on large scales horizon size Could be just the physics of large wavelength excitations of the lattice
  21. 21. How to describe this evolving background? gμ - metric on a higher dimensional manifold ν γab - metric on a sub-manifold . Standard picture: γab - induced, gμν - fundamental
  22. 22. How to describe this evolving background? I. R. Klebanov and L. Susskind, Nucl.Phys. B 309, 175 (1988) Take a string and chop it into N segments Let each segment carry non-vanishing P+ and P┴ P+ makes the string grow in length
  23. 23. Result • • Such a string builds this structure: • total length of the string grows as N • radius of the induced space grows as (Log N)1/2 • in the limit of N → the string becomes space filling ∞
  24. 24. How do particles propagate on this background? B Between any two points there are many possible paths A Feynman Path Integral Due to quantum fluctuations particle follows a jagged path Straight classical trajectory and paths nearest to it give the highest contribution Interference of many possible paths gives a straight propagation on average Our case: geometry of the lattice dictates the jaggedness of the path
  25. 25. Geometry of the lattice “Natural” Lattice Stack of branes Random Lattice • In all cases short distance physics is 2d (1d) • But the way one recovers 3d space at large distances is not the same
  26. 26. Geometry of the lattice Random Lattice Avoids preferred direction in space Avoids systematic violations of Lorentz invariance The preferred reference system may exist: the rest frame of the lattice (no more problematic than the preferred rest frame of the CMB)
  27. 27. Lorentz symmetry violation Lorentz invariance is restored on average on large distances However, small fluctuations of the path can have measurable effects for light propagating over large cosmological distances The effective speed of light might change Two simultaneously emitted photons of energy difference ΔE = E1 − E2 will arrive at the observer with a time delay Δt = t1 − t2
  28. 28. Gamma rays and Fermi satellite GRB Space-time foam Earth Fermi observed one 31-GeV and one 3-GeV photon arriving with the time delay of less than 1 sec Usually interpreted as the limit E* ≥ MPl
  29. 29. Fermi result and vanishing dimensions • Caveats: i. Only one event observed ii. Physics of the source poorly understood iii. Limit E* ≥ MPl valid only if linear corrections exist (LQG) iv. Both photons Eγ < TeV → no ceff (ΔE) v. High interaction probability for high energy gamma rays with CMB and infrared background photons (e+ e-)
  30. 30. Fermi result and vanishing dimensions • Fundamental objection: Discrete structures don’t automatically imply Lorentz symmetry violation Lorentz “invariant” discrete structure: LM
  31. 31. Regular vs. random lattice F. Dowker, J. Henson, R. Sorkin, gr-qc/0311055 Regular lattice in two different Lorentz frames (a) and (b) (Poison) Randomization is crucial: • One can’t tell what frame was used to produce sprinkling • Approximation is equally good in any frame LM
  32. 32. Effective speed of light B • To propagate from A to B with c on a straight line • It must move with ceff = √3 c along the sides A No problem in the Feynman path integral picture e- e+ e- e- In a short time (TeV-1) particle can move with v > c due to quantum effects Discrete structures don’t need to change an effective speed of light
  33. 33. LIV and vanishing dimensions We can’t take limits on LIV face value (E* ≥ MPl ) We simply do not understand how particles interact with the space-time structure at the fundamental level MPl = 1019 GeV doesn’t even make sense in 2d There is no ħ in MPl in 2d No quantum gravity in 2d? Classical gravity sufficient?
  34. 34. String theory solutions C. Callan, J. Maldacena, Nucl.Phys. B513, 198 (1998) N. Constable, R. Myers, O. Tafjord, Phys.Rev. D61 (2000) 106009 D-branes 1-brane 1-brane smoothly matching 3-brane 3-brane r→0 r→0 dz2 0 3-brane that looks like 1-brane around every poin
  35. 35. Experimental evidence? Experimental evidence for vanishing dimensions may already exists. Alignment of high energy secondary particles was observed in families of cosmic ray particles detected in the Pamir mountains (Russia and Tajikistan) 6 out of 14 events Altitude 4400 m Alignment is statistically significant for families with high energies E > 700 TeV which corresponds to ECOM > 4 TeV
  36. 36. Circle: Ellipse: Line: 3d event Somewhat planar Pure 2d event λ=0 λ > 0.5 λ=1 Parameter λ measures the degree of alignment
  37. 37. Experimental evidence? • Most of the aligned events originate just above the chamber • Thus, sea/ground level experiments can’t see the effect Mt. Kanbala (in China) E > 700 TeV , 3 out of 6 events Two stratospheric experiments E > 1000 TeV λ = 0.99 • STRANA superfamily, detected on board of a Russian stratospheric balloon • JF2af2 superfamily, detected on a high-altitude flight of the aircraft Concord
  38. 38. Possible LHC signature If the alignment in cosmic rays at ECOM > 4 TeV is not a fluke LHC might observe similar alignment
  39. 39. LHC signature If the fundamental high energy physics is 2d , the following must be true regardless of the exact underlying model: • Cross section changes due to the reduced phase space • Higher order scattering processes at high energies become planar • Jets of sufficiently high energy may become elliptic in shape
  40. 40. 3d momentum conservation If λde Broglie < L3 particle propagates locally in 2d, rather than 3d p┴ p|| p┴ branons Local description p|| To preserve 3d momentum of particles propagating over L >> L3 lattice absorbs p┴ and then re-emits it by the lattice back-reaction Non-local description Particle remembers its group velocity through quantum interference of several paths
  41. 41. 2d scattering For scattering to be 2d , wavelength of the mediator must be < L3 Momentum transfer Q2 > Λ32 Thus, only hard scattering can probe 2d structure of space
  42. 42. 2d vs 3d scattering Cross-section in 2d is a line (not a disk as in 3d) 3d cross section 2d cross section Phase space ~ dΩd: total cross-section reduced by a factor of 2
  43. 43. 2d vs 3d scattering Coulomb Potential: 3d → α is dimensionless 2d → α = L-1 3d 2d
  44. 44. 2d vs 3d scattering Drell-Yan cross section will drop as 1/E3 instead of 1/E2 once the 3d → 2d crossover energy is surpassed Drell-Yan process Limits from Tevatron data Λ3 > 800 GeV
  45. 45. Planar multijet events In 2 → 3 scattering with Q2 > Λ32 , all the virtual particles (propagators) must move in the same 2d plane 3d scattering 2d scattering Thus, outgoing partons must be in the same plane in the c.o.m. frame of the collision, thus drastically different from the 3d scattering
  46. 46. Planar multijet events • Local plane absorbs the initial p┴ momentum • Planar scattering happens in c.o.m. frame • Lattice transfers p┴ to the outgoing particles giving them boost • Planarity is preserved once we boost the particles back c.o.m. frame c.o.m. frame Impossible in com frame even in 3d Any three vectors originating from the common point and conserving overall zero momentum will be co-planar even in 3d
  47. 47. Planar multijet events 3d scattering 2d scattering Need 4-jets for acoplanar events in 3d Co-planar 4-jet events clear 2d signature
  48. 48. Elliptic Jets • If the lattice orientation is preserved over distances Λ-1QCD individual jets at very high energy may become elliptic in shape • Parton showers are ordered in Q2: the largest Q2 happen first • Showers may not be spherical (start planar then expand in 3d)
  49. 49. Lower dim cosmology • FRW metric in 2+1 dim is: • Equations: • Radiation dominated universe: • Solution:
  50. 50. Lower dim cosmology • FRW metric in 1+1 dim is: • But 1-kx2 can be absorbed into the definition of x • Any 1+1 dim metric is conformally flat (Φ may be promoted into dynamic field – dilaton)
  51. 51. Ambiguities • No reason to require good Newtonian limit in 2+1 dim: valid equations solution • No reason to require • No reason to require FRW metric either
  52. 52. Gravity waves signature In 2+1 dim any solution of the vacuum Einstein's eq. is locally flat • No local gravitational degrees of freedom • no gravitons in quantum theory • no gravity waves in classical theory
  53. 53. Gravity waves signature The characteristic frequency of gravitational waves produced at some time t in the past is redshifted to its present-day value f0 = f* a(t)/a(t0) Today’s frequency of primordial gravity waves created at T=T*
  54. 54. Gravity waves signature LISA should be able to see a cut-off in GW frequency LISA’s sensitivity
  55. 55. Conclusions • Fundamental problems have accumulated • Current ideas do not work • Time for radically new ideas We introduced the concept of evolving dimensions • Many problems simply disappear • Clear model independent observational signature
  56. 56. THANK YOU
  • quiron2011

    Mar. 12, 2015

The SEENET-MTP Workshop JW2011 Scientific and Human Legacy of Julius Wess 27-28 August 2011, Donji Milanovac, Serbia

Views

Total views

1,247

On Slideshare

0

From embeds

0

Number of embeds

36

Actions

Downloads

10

Shares

0

Comments

0

Likes

1

×