The String Theory Landscape
Technion, March 2005
Fulfills a long-standing dream: a unified theory of Einstein’s General Relativity and Quantum Mechanics, contains many features of the Standard Model of particle physics. Has resolved some of the great questions of quantum general relativity, esp. regarding black holes.
But while compatible with many facts of nature, any honest assessment would have to conclude that there have been no sharp predictions for future experiments, and not even any real understanding of the basic facts of the Standard Model.
Recently, for the first time, a suggestion how string theory might actually be related to nature, and a possibility for predictions. The key to this is the realization that theory possesses a huge number of states. This ``landscape” of string vacua is now being explored. It is possible that sharp predictions for experiment will soon emerge -- or that we will see that the theory is false.
(Last Nobel Prize –2004)
Encompasses the strong (quarks, gluons), weak (beta
decay) and electromagnetic interactions.
Completely describes all they physics conducted in
accelerators to the present time. No* discrepancies.
q, e, n, m,t,...
for processes involving Zo
f(x) is the probability for finding
a quark carrying a fraction
x of the proton
momentum. QCD predicts the
dependence on Q2
We know the composition of the universe, and it is peculiar:
Many proposals. I will focus on one, not because I am certain that it is correct, but because I believe it is the most promising.
The proposal has two pieces. But I will try to argue that within something called ``The Landscape” they form a unified whole. They may make distinctive predictions for experiment, which will be tested over the next decade.
A hypothetical symmetry between fermions and bosons.
If correct, explains:
A symmetry between fermions and bosons. As a theoretical possibility, discovered in string theory. But first considered as a possible phenomenon in nature for another reason: the ``hierarchy problem.”
At a basic level, the problem is one of dimensional analysis. (~=c=1).
Why isn’t MH¼ Mp?
Jackson (Lorentz): if electron had size ro, its self
energy » e2/ro. ro < 10-17 cm me = 1 GeV
If ro» 10-33 cm, me¼ Mp.
What’s wrong with this argument? In QED (Weiskopf, 1930’s),
ro effectively le; so self energy of order a£ me
(Jackson didn’t tell you that!)
What about the Higgs? – self energy is really e2/ro! So mass naturally of order Mp.
BUT IF PAIRED WITH BOSONS -- ok.
Supersymmetry must be a broken symmetry. The effective
size – scale of the breaking. This argument predicts
supersymmetry at scales not much above MW, MZ.
What should we see? For every boson, a fermionic partner; for every fermion, a boson.
Ecm = 14 TeV
Unification of Couplings
t(p -> e+po)>1033 years
Homework assignment: explore the idea that the fundamental
entities in nature are not point particles [quantum field theory]
but strings. Construct a Lorentz invariant theory of strings.
1. Many solutions exist with four flat dimensions, six curved.
These look, in some cases, very much like the Standard Model—
repetitive generations of quarks and leptons, Higgs…
2. Low energy supersymmetry as we might hope to see at
accelerators often emerges.
3. All of the solutions found in the homework are actually part
of a single, larger theory – only one consistent theory of
4. Many important insights into black holes, other issues in
quantum gravity, field theory (e.g. examples of exact duality
between electricity and magnetism).
When physicists complain that string theory hasn’t made contact with nature, these are the obstacles.
The discovery of supersymmetry would likely allow us to probe nature at a much deeper level.
Supersymmetry, as a theoretical possibility, was discovered in String theory, and it seems to play a fundamental role. But until recently, no idea what implications this should have for particle physics/the world around us: does string theory predict low energy supersymmetry?
In 2002 I spoke here and asked how might one decide this question. Difficult because no
scheme to decide which of many states of string theory might somehow be selected. I suggested look at features which might be true of many
String vacua. Now a serious proposal:
The cosmological constant is the energy density of the quantum vacuum. Einstein’s equations:
This integral doesn’t make sense. Presumably cut off by new
physics at some scale. E.g. supersymmetry, broken at
TeV, would give TeV4! 1052 too large!
String theory: at first sight, doesn’t help.
Even with broken supersymmetry, cosmological constant can be calculated and it is just as large as the field theory estimates suggest. This is closely related to many of the problems discussed earlier.
Vast array of vacuum states. A discretuum of values of the cosmological constant (Bousso, Polchinski; Banks, Dine, Seiberg).
Only in vacua with sufficiently small cosmological constant does structure (galaxies, etc.) form. Cosmological constant must be very small – at most about 10 times what is observed. Expect that if there is a distribution of cosmological constants, the cosmological constant is as large as it can be according to these considerations. This argument successfully predicted the observed cosmological constant.
Many find this form of explanation troubling, but it might be inevitable, much like arguing that the earth sun distance is as it is because, in the distribution of planetary distances from stars, only a distance of order an AU leads to conditions suitable for life.
Astronomers might call this ``observer bias.”
Pangloss in Candide (Bernstein/Hellman, others): ``Let us review chapter 11, paragraph 2, axiom 7: Once one dismisses the rest of all possible worlds, one finds that this is the best of all possible worlds.”
Weinberg referred to this idea as the``weak anthropic principle.” It is disturbing to many people. As Weinberg has said:
``A physicist talking about the anthropic principle runs the same risk as a cleric talking about pornography: no matter how much you say you’re against it, some people will think you are a little too interested.”
Recently, evidence has string theory seems to realize just the possibility envisioned by Weinberg. (Bousso, Polchinski; Kachru, Kallosh, Linde, Trivedi).
String theory: ten dimensional. Many classical solutions where space time is of the form M4£ X. X a ``Calabi-Yau” space; solves the source-free Einstein equation,
Rmn = 0.
On X, can include fluxes, analogous to magnetic fluxes. Like magnetic flux, quantized. Many possible fluxes (of order 100’s), can take many values (100’s). So vast numbers of possible states: 100300 for sake of discussion.If cosmological constant uniformly distributed, more than enough to give many with value close to that observed.
It is not absolutely clear that all of these would-be states exist within the theory, but if so, significantly alters our views of string theory (and what might be some sort of ultimate explanation of the laws of nature).
If these states really exist, and if the universe explores them in its
history, what can we do with such a theory?
Statistics (Douglas, Kachru and collaborators)
Count. Ask distributions of states with various
1. Cosmological constant (dark energy density)
2. Amount of supersymmetry
3. Gauge groups
4. Numbers of quarks and leptons
5. Weak scale (MW)
6. Particular features of supersymmetry breaking
Example (perhaps the most straightforward; still challenging)
The easiest states to study are those which have an approximate supersymmetry. One can count the states with small supersymmetry breaking and small cosmological constant. Extrapolating these results to large supersymmetry breaking suggests roughly equal numbers of supersymmetric, non-supersymmetric states. [This statement is controversial] The bulk of the states with small cosmological constant and small Higgs mass have TeV scale supersymmetry [or technicolor].
Nsusy is the number of supersymmetric states, e is a currently unknown small factor. Note that for small F, the latter two branches dominate. Each branch makes distinctive predictions.
What is striking is that with this input, string theory
may become predictive!
At the Tevatron at Fermilab, we are already exploring a new regime of energy and distance. In three years, we will start to explore much greater energies at the LHC. It is quite likely that we will stumble on remarkable, new features of nature: new symmetries, large extra dimensions, warping of space-time….
Such discoveries will be extraordinary in and of themselves. It is conceivable that they will tell us something about the character of physical law at far shorter distance scale.
Not typical of states in the landscape. But if the cosmological
constant is much larger than we observe, don’t form galaxies, stars (Weinberg, 1989). Perhaps question of why we are in a part of this very large universe with small cosmological constant is analogous to question of why fish are found in water, or why planets with life are at a particular range of distances from stars.
Astronomers might call this ``observer bias.” This explanation raises many questions, but at the moment is the best (only) one we have. The String Landscape is the first theoretical framework which realizes Weinberg’s proposal.