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Transcript
Firenze, 10/12/02
Sogni di una Teoria Finale Finita
G. Veneziano, CERN/TH







***************
The standard model & gravity
Classical and quantum infinities
Classical points/strings
Quantum string magic
****************
New cosmologies?
Large extra dimensions?
Outlook
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 nongravitational phenomena (exception: n-masses, mixing...)
Experiments @ 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...
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, (GUT’s)?
 relevance in (early) Cosmology

 Try
to add GRAVITY to the SM!

At first sight, there is no problem. Since 1916 we do have a very
elegant and successful theory of gravitational phenomena:
Einstein’s 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 PS1913+16, in full accordance with GR’s
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…..
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 Einstein’s equations (Black holes, Big Bang…)
Quantum Mechanics came out of these problems!
(e.g. Planck 1900)
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
infinite…but “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
Quantum Field Theory’s 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
g
k

gr
k
The recommended therapy for such a disease is called
renormalization, but it saves the patient only if he/she is not
too sick.....
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 Fermi’s theory
much below the W,Z scale.

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
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 stringlike 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?


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
(c=1 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

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
 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:
x5
E(p) ~1/R
w5=1
P5= h/R
E(w) ~ R
 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
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 theory’s 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”
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...



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
Dilaton’s rolling in PBB cosmology
V()
strong coupling
weak coupling
??
Initial


Present 0
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
Our horizon today
Now
only regions inside this
cone were able to “talk”
end of inflationary
phase = Big Bang
What about the real beginning ?
decelerating
expansion
Evolving size
of our Universe
Here
inflation
Time
A. Buonanno, T.
Damour & GV,
1999
Observable U today
t
H-1
Another
collapse,
big bang,
Universe
Our big bang
Onset of collapse/inflation
Initial chaotic sea of massless waves
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
 A cosmological
gravitational radiation background
=> detectable @ advanced LIGO/VIRGO, spherical
antennas?
 Amplification
 Relic
of EM perturbations => Bgal.?
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...
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 pdimensional surface called a Dirichlet p-brane
• If the SM gauge quantum numbers sit at the ends of open strings, we
get an effective (p+1)-dimensional gauge theory.
• If p=3 the brane could be our world with all SM particles stuck on it!
• Gravity, however, is carried by closed strings..These move
everywhere..
Our 3-brane
A hidden brane
A graviton
Open Dstrings
• 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?
• Newton’s law is only tested down to the mm. ….
x2
x5
FN , FC ≈ r -2
FC ≈ r -2
FN ≈ r -3
x1
• 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!
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




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...