The String Theory Landscape

Michael DineTechnion, 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

e+

e-

Zo

q, e, , ,

q,e,,,…

• 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

f(x) is the probability for finding a quark carrying a fraction x of the proton momentum. QCD predicts the dependence on Q2

e

p,Zo

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=-) [Probably the energy of the vacuum – Einstein’s Cosmological Constant. Why so small? ¼ 10-120 Mp

4]

Hypothesized AnswersMany 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 GeVIf ro » 10-33 cm, me ¼ Mp.

What’s wrong with this argument? In QED (Weiskopf, 1930’s), ro effectively e; so self energy of order £ 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.

Haven’t seen yet; if correct, must see at the Large Hadron

Collider, under construction at CERN (2007)

g

g

q

q~

q~

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 ! + e+ = 1029-1036 years

Unification of Couplings

Super Kamiokande (again!)

(p -> e+ o)>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(,) describes a string. (

2 -2)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, ’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 noscheme 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 atTeV, 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 =0. No Examples•Dynamics which gives =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

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 ``Calabi-Yau” space; solves the source-free Einstein equation, R = 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).

XX

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. 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

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, 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].

Three Branches of the Flux Landscape

An example of what we know: three classes of states with cosmological constant less than o and susy breaking scale F (in units of Mp = 1019 GeV, the Planck mass):•dN / Nsusyo F6

• dN / Nsusy o dF / F• dN / Nsusy o dF/ F3

Nsusy is the number of supersymmetric states, 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 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.

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.