Firenze, 10/12/02Firenze, 10/12/02

SogniSogni di una Teoria Teoria FinaleFinale Finita FinitaG. 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 & gravityThe 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: -masses, mixing...)

Experiments @ CERN, DESY, Fermi-Lab... have fully confirmed the validity/necessity of a QQFT 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!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 spectrumThe electron-proton systemThe 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 atomsThe 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 infinitiesQuantum 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

The recommended therapy for such a disease is called renormalization, but it saves the patient only if he/she is not too sick.....

k k

gr

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 SITUATIONA PARADOXICAL SITUATIONClassically, 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 THEORYFINITE THEORY

IS IT SUPERSTRINGS?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?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 ≥ 2T J Massless spinning strings are classically forbidden

Quantum String MagicQuantum String Magic

At the quantum level a scale appears.. Strings acquire a finite, minimal size (Cf. harmonic. osc.)

X ≥ (h/T)1/2 = ss

Classical inequality between J and M is corrected (Cf. h.o.)

J ≤ M2/2T + 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 cutoffProvides 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’ = s

2/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/ s

2 ~ 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

P5= h/R

E(p) ~1/R

E(w) ~ R

x5

w5=1

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 ? New Cosmologies ? (Finite theory => infinite time?)(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 = 8GN

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 cosmologyDilaton’s rolling in PBB cosmology

V()

??

Initial

weak coupling strong coupling

Present 0

Instead, as we go backward in time, Universe gets closer and closer to a trivial state (zero curvature, zero coupling)

Asymptotic Past TrivialityAsymptotic 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

HereHere

Our horizon todayTime

infl

atio

n de

cele

rati

ng

expa

nsio

n

end of inflationary phase = Big Bang

only regions inside this cone were able to “talk”

NowNow

Evolving size of our Universe

What about the real beginning ?

H-1

Our big bang

Onset of collapse/inflation

Initial chaotic sea of massless waves

Another collapse, big bang, Universe

Observable U todayA. Buonanno, T. Damour &

GV, 1999 t

Observable relics?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 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...

D-strings, D-branes, Large extra dimensions,Large extra dimensions,

lowering the quantum gravity scalelowering 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 (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..

• 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. ….

Our 3-brane A hidden brane

Open D-strings

A graviton

x5

FN , FC ≈ r -2

FC ≈ r -2

FN ≈ r -3

x2

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...