Download The String Theory Landscape

The String Theory Landscape
Michael Dine
Technion, March 2005
String Theory
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.
Outline
•What are we trying to explain: the Standard Model
and its successes.
•What are we trying to explain: limitations of the
Standard Model
•Experimental Outlook
•Cosmological mysteries
•String theory and its successes
•What makes string theory hard
•The landscape
•Theoretical Outlook
The Standard Model
(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.
10-3 precision.
PDG Wall Chart
Detailed Tests
• Zo physics at LEP, SLAC
q, e, n, m,t,...
e+
Zo
e-
q,e,n,m,t…
• Precision measurements of W§ masses at Fermilab
• Detailed QCD studies at HERA, Fermilab
• B physics, CP violation at Belle (KEK), Babar
Comparison of
theory, experiment
for processes involving Zo
e
g,Zo
p
f(x) is the probability for finding
a quark carrying a fraction
x of the proton
momentum. QCD predicts the
dependence on Q2
So What don’t we Understand?
Several puzzles:
•So many parameters? (About 17 – what kind of
fundamental theory is this?)
•Why is CP (T) conserved by the strong interactions?
•Why is MH << Mp?
•General relativity – doesn’t make sense when combined
with quantum mechanics?
A Puzzling Universe
We know the composition of the universe, and it is
peculiar:
•5% ordinary matter (baryons, i.e. p’s and n’s
•30% dark matter (p=0) [What is it?]
•65% dark energy (p=-r) [Probably the energy
of the vacuum – Einstein’s Cosmological
Constant. Why so small? L ¼ 10-120 Mp4]
Hypothesized Answers
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.
•Supersymmetry
•String Theory
Supersymmetry
A hypothetical symmetry between fermions and bosons.
If correct, explains:
•Why MW << Mp (hierarchy puzzle)
•What is the dark matter
•(Predicted) one of the gauge couplings (unification)
•(Predicted) small neutrino masses
•Why we are here.
String Theory
•Unifies gravity and the Standard Model in a
consistent quantum mechanical framework
•In principle, explains the parameters of the
Standard Model.
•Supersymmetry fits in naturally – a prediction?
If so, dark matter,…
•Cosmological constant (dark energy) calculable
in principle.
What is supersymmetry?
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 MH ¼ Mp?
Why isn’t me = 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, me ¼ 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.
l
g
q
l
~
q
g
~
g
q
l
Haven’t seen yet; if correct, must see at the
Large Hadron
Collider, under construction at CERN (2007)
Ecm = 14 TeV
Significant indirect evidence:
•Lightest supersymmetric particle: accounts for the dark matter
(currently several experimental searches)
•Unification of couplings
The gauge couplings of the strong, weak and electromagnetic
interactions depend on energy. With supersymmetry, at
very high energies, assuming that they are the all the same
at a very high energy scale, predict the value of the strong
coupling. Unification also accounts for:
•The quantization of electric charge
•The excess of matter over antimatter in the universe
•Neutrino masses of roughly the right size
And predicts: The proton is radioactive.
p ! p + e+ t= 1029-1036 years
Unification of Couplings
Super Kamiokande (again!)
t(p -> e+ po)>1033 years
If discovered, next step: the ILC
(International Linear Collider)
Outcomes of a Discovery:
•Discovery and understanding of a new fundamental
symmetry.
•Rich new spectroscopy
•Detailed understanding of the dark matter, much as
we currently understand the element abundances
•Quite possibly an understanding of why there is matter
in the universe.
What is String Theory?
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.
Hints:
•
Look in Marion for non-relativistic case.
•
XI(s,t) describes a string.
(t2 -s2)XI =0 -- string equation
Homework Solution:
1. Five Lorentz invariant solutions exist.
They always contain Einstein’s
gravity, often contain gauge particles like
W’s, Z’s, g’s… Fully consistent quantum mechanically.
Most have supersymmetry.
2. If all dimensions are flat, ten dimensions only.
Extra Credit
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
quantum gravity?
4. Many important insights into black holes, other issues in
quantum gravity, field theory (e.g. examples of exact duality
between electricity and magnetism).
But: (why is string theory hard?)
•At classical level, too many solutions. Different gauge
groups, numbers of quarks, amount of
supersymmetry. What principle distinguishes?
•At quantum level, the solutions which might can’t be
relevant to nature can’t be studied in a sensible
approximation.
When physicists complain that string theory hasn’t
made contact with nature, these are the obstacles.
Supersymmetry and String
Theory
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 Landscape.
The most serious failure of all:
The cosmological Constant
The cosmological constant is the energy density of the
quantum vacuum. Einstein’s equations:
Naively,
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.
Solutions of the Cosmological
Constant Problem
•Symmetry which gives L =0.
No Examples
•Dynamics which gives L =0.
No Examples
•Selection among a landscape of vacua (Banks,
Weinberg, Linde, Vilenkin…) A dramatic
prediction (1988)
What is a Landscape?
Vast array of vacuum states. A discretuum of values of
the cosmological constant (Bousso, Polchinski; Banks,
Dine, Seiberg).
V
f
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.”
The Landscape of String Theory
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 ``CalabiYau” space; solves the source-free Einstein equation,
Rm n = 0.
X
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
properties:
1.
2.
3.
4.
5.
6.
Cosmological constant (dark energy density)
Amount of supersymmetry
Gauge groups
Numbers of quarks and leptons
Weak scale (MW)
Particular features of supersymmetry breaking
How to make predictions? Look
for correlations.
Example (perhaps the most straightforward; still challenging)
Cosmological constant
Supersymmetry
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, nonsupersymmetric states. [This statement is controversial] The
bulk of the states with small cosmological constant and small
Higgs mass have TeV scale supersymmetry [or technicolor].
Three Branches of the Flux
Landscape
An example of what we know: three classes of states
with cosmological constant less than Lo and susy
breaking scale F (in units of Mp = 1019 GeV, the Planck
mass):
•dN / NsusyLo F6
• dN / Nsusy Lo dF / F
• dN / Nsusy e Lo dF/ F3
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.
Further work is needed to decide which (if any) of these
possibilities is realized. But these problems may be tractable.
Would like to know:
•Relative numbers of supersymmetric, non-supersymmetric
states
•Selection effects: vacuum stability, proton stability,
cosmology (more observer bias needed?)
•More detailed predictions. E.g. with greater understanding,
more detailed phenomenological predictions, such as precise
form of susy spectrum (Dine, Gorbatov, Thomas, O’Neil, Sun)
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 spacetime….
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.
Supersymmetric Searches (PDG)
Why is the cosmological constant
small?
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.