Transcript dreams of a finite theory - Indico

DREAMS OF A FINITE
*)
THEORY
Gabriele Veneziano
(CERN-PH/TH & Collège de France)
*) Adjusted from Steven Weinberg’s:
DREAMS OF A FINAL THEORY
Outline
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Forces & particles: carriers & bricks
How did we get there?
Looking at history backwards:
a) From the EW theory to Fermi’s
b) From QCD to the old string
Classical vs. quantum strings: the bad news
Classical vs. quantum gravity: the clash
Classical vs. quantum strings: the good news
Dreams of a finite theory:
black holes, cosmology, extra dimensions…
PLAYERS
FORCE
= carries
= feels
CARRIERS
Gluons g
W,Z Graviton
BRICKS
?
STRONG
EM
WEAK
GRAV.
??
?
H
q
lCh.
n
nR ?
Evolution of our understanding
Electric
Magnetic
}
t
Classical
ElectroMagnetism
(Maxwell)
QED
EW
Weak
SM
Fermi
1934
Nuclear
QCD
String
Gravity
Classical
General
Relativity
(Einstein)
String
1984
1968
QGD
We shall follow
the green arrows
EWT (early70’s)
Neutron bdecay
n
d
u
d
e
p-
u
e
n
n
Wu u
d
Charged-pion decay
d
Fermi (1934)
n
p
p
pointlike
interaction
m-
W-
is the killer
pn
mn
No surprise, a posteriori, that Fermi was led
to his effective theory of weak interactions
…and that such a theory cannot be valid at
very short distances
What about the neutron, the proton, the pion?
From QCD to the old string
quark
antiquark
quark
antiquark
Quarks are held together by the confining potential of a
colour-electric flux tube
r
E = M c2 = T r
(T= dE/dr = Tension)
Naïve classical picture:
J = M v d < c-1 T r2
J < a’ M2
(a’ = c3 /2pT)
NB: no massless states with J > 0 !
J
J = a’ M2
forbidden
allowed
M2
Smells of a déjà vu…
The linearly rising Regge trajectories of early sixties!
J/h
dJ/dM2 ~ 0.9 GeV-2
fermions
11/2
bosons
r
p
D
1
N
M2
No surprise that a theory of strings was
discovered starting from some striking
properties of the hadronic world
…and that such a theory differs from
QCD at very short distances
(like Fermi vs. GSW)
So far we neglected Quantum Mechanics…
Classical physics is valid for large quantum numbers,
highly excited levels
When the QCD flux tube is long compared to its
transverse size, it can be considered as onedimensional, a string-like object
Indeed strings do provide an effective description of
QCD at large distances
By contrast..
Large quantum effects occur at small quantum
numbers, i.e. for the lightest states
These depend on exactly what kind of string one is
talking about, on its thickness, on what makes it or
sits at its ends
The old string of the sixties was the simplest
possible one…
String Theory = Theory of
(Quantum-Relativistic) Strings
Obvious generalization of relativistic point particles
(this is what led us, eventually, to QFT and to the SM!)
Spoint = - mi c (length) + inter.
model-dependent
Species-dependent
------------------------------------no inter. needed
Sstring = - T (Area).
Universal
Classical motions minimize length, area
Quantum surprises
A vibrating string is just an infinite collection
of harmonic oscillators whose characteristic
frequencies are multiples of a fundamental
frequency
Its quantization is almost as simple as that of
a single harmonic oscillator, however…
“Casimir Energy” of fundamental string
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The zero-point energies of each harmonic oscillator
in the string add up, …to something negative
Massless states become possible, actually
inevitable, even if they have up to 2h worth of J.
States with half-integer spin are also necessary
for consistency => superstrings and (theoretical)
discovery of supersymmetry in early seventies…
The quantum spectrum
(@small coupling)
J
Classical boundary
fermions
J
Classically
forbidden
2h
3/2h
Classically
allowed
h
1/2h
M2
2h
The bad
quantum news: no such states in hadronic physics !
M2
J/h
dJ/dM2 ~ 0.9 GeV-2
fermions
11/2
bosons
r
p
D
1
N
M2
Furthermore…
The string was “IT” there was nothing more basic
inside, no internal structure, no constituents
QCD has quarks and gluons, its string is a derived
object, endowed with a finite thickness, made of
pointlike constituents
The final verdict, as always, belonged to experiments
It came clear from the study of hard-processes
~1974: strings are out!
Quarks and gluons are there and, till these
days, look like elementary, point-like objects
The F-string is just an effective description
of the complex phenomenon of confinement
Finding the true QCD string is still an area of
intensive theoretical research
Classical vs. Quantum Gravity: the clash
Gravity couples to energy
(basis of GR’s Equivalence Principle)
At low-energy (LHC?) it is weak, negligible
At the quantum level, very energetic quanta
can be created and destroyed over short
distances or time intervals
If these processes are not sufficiently
suppressed they lead to uncontrollable
infinities even for low energy processes
1984: strings are back!
Casimir Energy of the F-String
The massless states of the superstring nicely
fit with what is required for the carriers of
gauge and gravitational forces
A disaster for the old string becomes a first
tremendous bonus for a theory of all
interactions

PLAYERS
FORCE
= carries
= feels
CARRIERS
Gluons g
W,Z Graviton
BRICKS
?
STRONG
EM
WEAK
GRAV.
??
?
H
q
lCh.
n
nR ?

Like
Minimal quantum size
an harmonic oscillator, a string has a
mimimal quantum size ls = Dx = h/T
This new fund.al constant (besides c and h)
exponentially damps pvirtual > h/ls
Quantum mechanics, rather than clashing
with General Relativity, frees gravity from its
divergences and provide a FINITE theory*)
a second extraordinary bonus!
*)Cf. QM’s solution of BB rad. and atom stab.

Fundamental
Extra dimensions
strings cannot be quantized in any
number of space-time dimensions
For superstrings 9 space and 1 time coordinates are
needed for quantum consistency
Rather than a killer this is now seen as an
opportunity: if 6 of the 9 spatial dimensions are tiny
they can provide a new mechanism to generate gauge
interactions (of the GUT type) a la Kaluza-Klein
If they are not that small they can modify gravity
at sufficiently short distances, e.g. below 1 mm.
and/or provide new physics even at LHC energies
Can we have the cake and eat it?
We want constituents where they help (QCD)
and dispose of them where they harm (QGD)!
Distinguish two kinds of strings!
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Scale down the characteristic size of fundamental
strings from 10-13 to 10-32 cm
Quarks (and all other players) are “slim” F-strings.
Protons, neutron, pions are “fat” QCD strings!
We have almost point-like quarks, but there is new
physics just above the Planck length scale
lP =
GNh/c3 ~ 10-33 cm
Let’s have a quick look at some of it!
Can string theory solve
the information paradox?
Hawking claims (used to claim?) that
black holes turn pure quantum states into
mixed thermal states thereby producing
a loss of quantum coherence
String/Black-Hole correspondence?
S. Hawking (1974): black holes have T and S!
TH-1 ~ M = RS , SBH ~ RS2 ~ M2
M
Sstring ~ M , Tstring< THagedorn
R S > ls
Black Holes (= Strings? )
R S < ls
Strings ≠ BH
RS = ls
gs ~ gauge coupling
String theory looks
perfectly consistent with
quantum coherence
Information Paradox MUST
be solved: exactly how?
Fate of black hole evaporation
through Hawking radiation
M
trajectory of evaporating BH
Black Holes
RS = ls
Strings
gs
Would be singularity: avoided thanks to ls≠0?
Fate of Big Bang singularity
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Big bang singularity is avoided too if the curvature
radius (basically H-1) cannot shrink below ls
Reopens question of the beginning of time and
allows one to consider new cosmologies whereby a
long era preceded/prepared a big bang-like event
(see e.g. Scientific American, May 2004 issue)
time
Present horizon
now
Present distance from remote cluster
Qui
H-1
End of inflation
Towards the Big Bang, t=0
space
STANDARD INFLATION
time
Present distance from far cluster
Our horizon today
now
Here
H-1
ls
space
end of pre-bang phase
PRE BIG BANG
Towards empty space
@ past infinity
Will all this bring our understanding of
gravity, astrophysics and cosmology up
to particle-physics standards?
Will it unify our understanding of all
interaction within a single consistent
framework?
A dream that may
remain just that for
a while…