Firenze, 101202 Sogni di una Teoria Finale Finita G. Veneziano, CERNTH

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Firenze, 10/12/02Sogni di una Teoria Finale
FinitaG. Veneziano, CERN/TH

• The standard model gravity
• Classical and quantum infinities
• Classical points/strings
• Quantum string magic
• New cosmologies?
• Large extra dimensions?
• Outlook

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The standard model gravity

• By combining the principles of Quantum Mechanics
  and Special Relativity, the Standard Model (SM)
  of particle physics provides, so far, an accurate
  description of all non-gravitational phenomena
  (exception n-masses, mixing...)
• Experiments _at_ CERN, DESY, Fermi-Lab... have fully
  confirmed the validity/necessity of a QFT
  description (radiative corrections are needed!)
• What about gravity? Superficially, gravity and
  electromagnetism, the two long-range forces, look
  very similar.. however...

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• Gravity is weak For the H-atom
• FN /FC m1m2 /q1q2 10-40
• Gravity is usually neglected for microscopic
  systems
• Gravity always adds up Becomes strong for large
  bodies while EM forces cancel out for neutral
  systems
• relevance in Astrophysics
• Gravity couples to energy
• FN , FC become comparable at high energies (
  1018 GeV)
• relevance for theories beyond the SM, (GUTs)?
• relevance in (early) Cosmology
• Try to add GRAVITY to the SM!

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• At first sight, there is no problem. Since 1916
  we do have a very elegant and successful theory
  of gravitational phenomena
• Einsteins General Relativity (GR)
• Like the standard model of non-gravitational
  phenomena, GR has now been tested to high
  accuracy, last but not least through (indirect)
  evidence for the emission of gravitational waves
  by binary pulsar PS191316, in full accordance
  with GRs expectations
• Many competitive theories of gravity have been
  ruled out, as it is the case for most
  alternatives to the SM
• Furthermore, SM and GR are deeply rooted in
  similar physical principles
• Gauge-Invariance for the SM
• Equivalence Principle for GR
• Difference appears when we consider infinities..

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Classical infinities

• Classical theories are often singular.
  Examples
• The black body spectrum
• The electron-proton system
• The EM self energy of a point-like charge
• Solutions to Einsteins equations (Black holes,
  Big Bang)
• Quantum Mechanics came out of these problems!
• (e.g. Planck 1900)

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Fate of singularities in QM

• The black body spectrum becomes finite Planck
  spectrum
• The electron-proton system too stability of
  atoms
• The EM self energy of a point-like charge is
  still infinitebut not as much (log r instead
  of 1/r)
• What about the singularities of CGR? Are they
  helped by QM?
• One would guess answer to be positive but
  actually we do not know

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Quantum Field Theorys infinities

• Ultraviolet divergences virtual processes in
  which very energetic quanta are emitted and
  reabsorbed are not sufficiently suppressed in QFT
  and give infinitely large contributions to
  observables such as masses, couplings
• The recommended therapy for such a disease is
  called renormalization, but it saves the patient
  only if he/she is not too sick.....

g
gr
k
k
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• Gauge theories -such as the SM- are OK, i.e. all
  infinities can be lumped into a finite number of
  observables.
• One obtains a renormalized QFT, i.e. a theory
  containing a finite number of uncalculable
  parameters which have to be taken from
  experiments. The rest is predictable (Cf.
  precision tests of the SM).
• Since gravity couples to energy, UV-divergences
  are more severe in GR than they are in the SM.
• For GR, UV infinities cannot be lumped into a
  finite set of observables and predictivity is
  lost. Present attitude GR is just an effective
  low-energy theory, like Fermis theory much below
  the W,Z scale.

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A PARADOXICAL SITUATION

• Classically, gauge and gravitational interactions
  look very similar but
• While gauge theories can be promoted to the
  level of a full quantum theory, the Standard
  Model, General Relativity cannot.
• A unified treatment of gravitational and
  non-gravitational interactions at the full
  quantum level appears to call for a
• FINITE THEORY

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IS IT SUPERSTRINGS?(see Brian Greene, The
Elegant Universe, Vintage, 2000)

• For more than 30 years particle theorists have
  played with strings
• In retrospect, some of us were led to them
  because string-like excitations appear
  (experimentally and according to QCD) in hadronic
  physics
• Since 1984 (super)strings have been taken as a
  serious candidate theory of all interactions.
• Why?

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• At first sight, the concept of string-like
  particles appears to be a harmless/boring
  extension of the concept of point-like particles.
• Rather than mass, strings have a tension T
  energy/length (c1 throughout). They can also
  rotate and thus carry angular momentum, J.

• There is no characteristic length scale in
  classical string theory (M /T L is arbitrary,
  point-like limit is trivial)
• Classical strings have any size/mass!
• Also, they cannot have J w/out a finite size,
  hence w/out M. One finds
• M2 2?T J
• Massless spinning strings are classically
  forbidden

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Quantum String Magic

• At the quantum level a scale appears..
• Strings acquire a finite, minimal size (Cf.
  harmonic. osc.)
• ?X (h/T)1/2 ?s
• Classical inequality between J and M is corrected
  (Cf. h.o.)
• J M2/2?T a0 h , a0 1/2, 1, 3/2, 2.
• Quantum strings become serious candidates for a
  finite theory of all known interactions.
• Provides an UV cutoff
• Provides the carriers of all fundamental forces

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• Strings like/need 3 (9 or 10) dimensions of
  space but....
• Unlike points, strings do not distinguish a
  circle of radius R from one of radius R ?s2/R.
  The minimal physical value of R is ?s. This 3rd
  miracle is related to string winding
• The arbitrary parameters of QFT are replaced by
  fields, e.g.
• ?????GN T lP2/ ?s2 e gs2
• where ? is a scalar field, the dilaton, whose
  dynamics should eventually determine ??
• From the experimental value of ??we deduce
• ?s 10 lP 10-32 cm
• At this scale (1017-1018 GeV) gravity and gauge
  interactions are unified even at the quantum level

x5
E(p) 1/R
w51
E(w) R
P5 h/R
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What if Superstrings?

• Which are the physical implications of
  superstring theory?
• Hard to answer, we can only make educated
  guesses based on some very general features of
  QST
• i) Strings like to live in D 4 dimensions of
  space-time
• ii) String theorys finiteness comes with
  modifications of QFT at short-distance/high
  energy (i.e. at ?s , Ms )
• Implications for
• 1. Very early cosmology (high T high E)
• 2. Low-energy experiments if we can lower the
  string scale and/or if some of the extra
  dimensions are large

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New Cosmologies ? (Finite theory infinite
time?)

• The problems of standard cosmology come from 2
  reasons
• Time had a beginning
• The expansion is decelerated
• Standard inflation avoids those problems by
  modifying 2 through an effective cosmological
  constant which has later (almost?) died...
• In string theory the big bang singularity is very
  likely removed by ?s 0
• Time needs not to have started at the big bang.
• If time had a longer history other possibilities
  open up...

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• In the very early universe the dilaton may have
  played an important role
• While today it is (probably) frozen and massive
  (?????GN e) nothing prevents it from
  having evolved cosmologically from the weak
  coupling (e? 0) region to where it is now (
  figure)
• While so doing ? can provide a new mechanism for
  inflation. Einstein-Friedmann equation for the
  expansion rate
• 3 H 2 8??GN??
• allows for solutions with growing
• GN e ? and H (hence inflationary!)
• The Universe inflates as interactions become
  stronger and stronger

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Dilatons rolling in PBB cosmology

• V(?)

strong coupling
weak coupling
??
?
?
Initial
Present ?????0
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• Instead, as we go backward in time, Universe gets
  closer and closer to a trivial state (zero
  curvature, zero coupling)
• Asymptotic Past Triviality
• How do we then see the birth of our Universe in
  this new cosmology?
• I will try to illustrate that in a few cartoons..
• For more details see
• M. Gasperini and G.V.hep-th/ 0207130
• Web site http//www.ba.infn.it/gasperin

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Our horizon today
Time
Now
Here
only regions inside this cone were able to talk
decelerating expansion
Evolving size of our Universe
end of inflationary phase Big Bang
inflation
What about the real beginning ?
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Observable U today
A. Buonanno, T. Damour GV, 1999
t
H-1
Another collapse, big bang, Universe
Our big bang
Onset of collapse/inflation
Initial chaotic sea of massless waves
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• Observable relics?
• It looks almost incredible that relics from
  before the big bang
• could be seen today.. This claim however is not
  different
• from the usual one that CMB anisotropies and LSS
  reveal
• primordial quantum fluctuations amplified during
  inflation.
• It is related to the phenomenon by which large
  scale fluctuations freeze out during inflation
• Some examples

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• A cosmological gravitational radiation background
  detectable _at_ advanced LIGO/VIRGO, spherical
  antennas?
• Amplification of EM perturbations Bgal.?
• Relic axions w/ an interesting spectrum of large
  wavelength perturbations LSS, CMBA, DM?
  Boomerang, Maxima, Dasi etc. data on acoustic
  peaks are already challenging the simplest PBB
  models, but massive axions decaying before PNS
  can save the day...

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D-strings, D-branes, Large extra
dimensions,lowering the quantum gravity scale

• Recall Neumann and Dirichlet b.c.s for a
  vibrating open string free ends vs. fixed ends
• In superstring theory we can consider a mixed
  case only some coordinates are fixed the end
  points can move only on a p-dimensional surface
  called a Dirichlet p-brane
• If the SM gauge quantum numbers sit at the ends
  of open strings, we get an effective
  (p1)-dimensional gauge theory.
• If p3 the brane could be our world with all SM
  particles stuck on it!
• Gravity, however, is carried by closed
  strings..These move everywhere..

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Our 3-brane
A hidden brane
A graviton
Open D-strings

• If the SM lives on the brane and gravity lives
  everywhere new possibilities arise
• The extra dimensions are only felt by gravity,
  and only when we probe it at distances smaller
  than the size of the extra dimensions. How large
  can they be?
• Newtons law is only tested down to the mm. .

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x2
x5
FN , FC r -2
FC r -2
FN r -3
x1
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• At short distances gravity feels the extra
  dimensions and grows with a higher power of 1/r
  than the gauge force...hence gets strong at a
  larger distance (lower energy) scale....
• Alternatively gravity is weak at large distance
  because it decreases much faster than 1/r2 below
  the length scale Rcomp
• For instance, with 2 dimensions of radius R
  exclusively reserved for gravity,
• R 1mm E(Strong Gravity) few TeV
• Strong gravity at the LHC?
• In optimistic cases, lots of new phenomena can be
  expected at LHC energies!

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Outlook

• Physics at the beginning of this century reminds
  us of the situation at the beginning of last
  century a Standard Model was there, based on
  Newton and Maxwell, and many thought that physics
  was over
• Two major revolutions came them and changed
  forever our understanding of Nature...
• Is this pattern going to repeat itself?
• I think that the infinities of QFT, of classical
  GR, and of quantum gravity, cannot be played down
  and require a profound revision of our
  theoretical frameworks.
• Superstrings are the best/only example we have
  today to bring about a truly unified quantum
  description of all interactions

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• The challenge convert a beautiful
  theoretical/mathematical framework into something
  predictive ... and testable.
• Many unresolved puzzles in gravitation and
  cosmology (big bang, black holes, ?cosm..)
  probably do need a consistent way to combine GR
  and QM
• Insisting on theoretical consistency has paid off
  enormously towards understanding EW and Strong
  interactions..but it took some 50 years of hard
  experimental theoretical work to produce the SM
  of particle physics
• Insisting on finiteness will probably pay as
  much, if we are able to spot the right
  theoretical and experimental ideas
• A dream that may remain just that for a while...