1. String Theory CERN HST 2004 lectures
J.P. van der Schaar
CERN Theory Division

2. Outline Why do we need string theory What is string theory
Latest developments
Strings and particle physics
Strings and black holes
Strings and space-time
Outline of Saturday morning lectures
7/19/2004
CERN HST 2004

3. Roads to Quantum Gravity
Planck scale physics: Mp~ 1019 GeV , Lp ~ cm
Particle physics: QM without gravity
Cosmology: gravity without QM
Particle physics: higher energies
Cosmology: backwards in time
LHC: 104 GeV
Inflation ~ 1016 GeV
7/19/2004
CERN HST 2004

4. The physics of QG Ruv – ½ guv R = k <Tuv>
Describe graviton and Planck scale quantum scattering
Resolve the origin of our universe (BB)
Explain Black Hole microphysics
Describe the fundamental quantum structure of spacetime
Ruv – ½ guv R = k <Tuv>
Classical spacetime
Quantum matter
Unified theory of particle physics
Hierarchy problem (MW << MP)
Value of the cosmological constant
7/19/2004
CERN HST 2004

5. Quantizing gravity
Gravity is non-renormalizable, the infinities cannot be consistently removed (GN = Mp-2)
What does it mean to quantize space and time?
Space-time foam, shortest distance?
We have to be more creative!
7/19/2004
CERN HST 2004

6. From points to strings
Origin of QFT infinities: pointlike interactions (“local”)
Idea: smearing/spreading of the interactions (“non-local”)
Result: finite scattering amplitudes (‘UV regulated’ 2d Feynman diagrams, tubes)
Replaced points by loops of string: ultimate elementary stuff, presumably not made out of something else
7/19/2004
CERN HST 2004

7. String Theory Strings have internal dynamics: they can vibrate
Wonderful unifying opportunity: a single string can potentially describe many different “particles”
Among the different vibrational patterns of the quantum string, one of them has the properties of a massless spin two particle, i.e. a graviton, implying that string theory is a finite theory of quantum gravity!
7/19/2004
CERN HST 2004

8. Strings vs. QFT String theory is a finite theory and “predicts”:
QFT predicts anti-particles
Not very unique, many possible interactions can be introduced at the interaction points
Can not incorporate gravitons
String theory is a finite theory and “predicts”:
Gravity (closed strings)
Gauge particles (open strings)
Infinite set of (very) massive particles
Supersymmetry
Extra space-time dimensions
Very unique structure, (non-local) interactions are not arbitrary
because they are described by the same free string
7/19/2004
CERN HST 2004

9. The string scale Among the massless closed string states: graviton
To reproduce weak graviton interactions (GN~ Mp-2) the string tension should be close to the Planck mass
Correspondingly the string length should be close to the Planck length and excited string states have masses close to the Planck mass
This is good news: the infinite number of massive states described by the string are way to heavy to be relevant for our low energy world
String parameters: gs, Ls
GN = (gs Ls)2 ~ Mp-2
7/19/2004
CERN HST 2004

10. The bad news
The simplest (bosonic) string theory can not describe fermions and is only consistent in 25+1 dimensions
This lead to the discovery of supersymmetry and superstring theory
Superstring Theory does contain fermionic excitations, it predicts supersymmetry, but is only consistent in 9+1 dimensions!
Five consistent (closed + open) superstring theories
Obviously our universe is 3+1 dimensional, so string theory has to be wrong, or perhaps…
Heterotic SO(32) : closed superstrings
Heterotic E8 x E8 : closed superstrings
Type I : open and closed superstrings
Type IIA : closed superstrings
Type IIB : closed superstrings
E. Witten: “If one of the 5 theories describes our universe, who lives in the other four?”
7/19/2004
CERN HST 2004

11. Extra dimensions
Imagine a universe that is 2-dimensional: time + left/right
Now imagine that our world actually contains a small extra 3rd dimension that is curled up
Claim: if the extra 3rd dimension is small enough 2-dimensional low energy observers will not be able to detect it !
Particles can travel in the extra dimensions and because of their wavelike character this motion in the extra dimensions is quantized giving rise to Kaluza-Klein particles with masses M ~ 1/R
Add photos of Kaluza-Klein somewhere
Going back to our 4-dimensional universe: we can not exclude the possibility that our universe contains small extra dimensions
7/19/2004
CERN HST 2004

12. String compactifications
Being a fully unified theory of quantum gravity and all particles and interactions one goal should be to reproduce 3+1 dimensional SM physics
Typical size of the compactification manifold is string scale to make sure that KK states due to the compact direcions are very heavy
Done in steps: first try to obtain the Minimal Supersymmetric SM in 3+1 dimensions by curling up 6 extra dimensions without breaking all SUSY: Calabi-Yau manifolds
The spectrum of particles in 3+1 dimensions depends crucially on the shape and size of the Calabi-Yau manifold
The good news: some of these CY-compactifications look a lot like our world!
The bad news: millions of options, looking for a needle in a haystack!
7/19/2004
CERN HST 2004

13. Extra dimensions and SUSY
Could have interesting low energy (TeV) particle physics consequences (LHC)
Superpartner detection (SUSY breaking scale)
Detecting (large) extra dimensions
Interestingly enough, gravity has only been tested at the 1/10 mm level and therefore allows extra dimensions to be rather large, if the other fields are restricted to our 3+1 dimensional world (brane-world scenarios)
In this lecture I want to concentrate on the true nature of string theory and what it has taught us so far about Planck scale physics (i.e. quantum gravity)
7/19/2004
CERN HST 2004

14. Strings and QG
String theory is perturbative by definition (whereas QFT is at least defined non-perturbatively)
One fixes the background space-time and then considers the propagation of string states perturbatively
String coupling gs determines the strength of the interactions (determined by the fixed space-time background)
Roughly speaking strong string coupling corresponds to strong gravitational environments
Many interesting questions we would like to answer involve strong string coupling at some point, for instance when considering the Big Bang, understanding black holes etc.
Basic question:
WHAT IS STRING THEORY?
7/19/2004
CERN HST 2004

15. Non-perturbative strings
Make use of the correspondence principle: low-energy superstrings can approximately be described by supergravity theories
Supergravity theories have classical, soliton solutions called black p-branes
Correspond to generalized black holes solutions carrying mass and charge in just the right ratio, such that there is no force between two p-branes
Interpretation of these solutions in string theory: surfaces on which open strings can end, so-called D-branes (Dirichlet boundary conditions)
1,2,………N
7/19/2004
CERN HST 2004

16. Black Hole Physics
When an objects mass is localized within the Schwarzschild radius, it is considered a black hole
When Planck scale energies are involved this also seems to apply to elementary particles
Black holes have mass, charge and can rotate, but that’s it: “Black holes have no hair”
BH (Sun): TH ~ K
BH (Electron): TH ~ 1052 K
Entropy BH (Sun) ~ 1077
Entropy Universe ~ 1094
Black holes emit Hawking radiation
Thermodynamical temperature and entropy, but without a stat.-mech. microscopic interpretation!
Suggests information is lost inside a black hole
T ~ 1/GNM , S ~ A/4GN
7/19/2004
CERN HST 2004

17. Strings and black holes
Special charged black holes can be modeled in string theory using D-branes
The special (SUSY) properties of these black holes allows one to follow its behavior as we lower the string coupling
At weak coupling one can count the open string degrees of freedom on the D-branes and remarkably this reproduces the black hole entropy!
In the D-brane picture there is no information loss problem!
7/19/2004
CERN HST 2004

18. The Holographic Principle
In the absence of gravity thermodynamical systems have an entropy that scales with the volume (extensively)
In the presence of gravity this is no longer true, since by adding more and more energy into a finite volume, at some point a black will be formed and we know that the black hole carries one degree of freedom per Planck AREA
This lead to the conjecture that QG is a holographic theory, i.e. the fundamental degrees of freedom live in one dimension less and reproduce our world holographically
CAN WE FIND CALCULABLE EXAMPLES ?
IS STRING THEORY HOLOGRAPHIC ?
7/19/2004
CERN HST 2004

19. Strings and Holography
Consider D-branes again
Geometrical (space-time) description
Open string description
Take a low energy limit
Geometry reduces to Anti-de Sitter
Open strings reduce to gauge theory
But these two descriptions should describe the same physics!
AdS space-time corresponds to the curved geometry of a negative cosmological constant
AdS/CFT correspondence: string theory on AdS space-time can equivalently be described by a gauge theory in one dimension less
7/19/2004
CERN HST 2004

20. Strings and QCD Why do we never see quarks?
Qualitative answer: QCD coupling becomes stronger as the distance between quarks increases (field lines squeeze)
No quantitative control (calculate hadron masses)
Historical reason for String Theory: QCD string
AdS/CFT correspondence relates string theory on AdS space-time to a SUSY version of QCD
Potential to learn about strongly coupled QCD using gravity/String Theory
AdS strings
Boundary YM
7/19/2004
CERN HST 2004

21. Stringy spacetime Strings can wrap compact dimensions
Two kinds of states in the non-compact dimensions: KK-momentum modes and winding modes (quantized)
Observer will not be able to distinguish these states!
Radius of compact dimension ambiguous!
Mw ~ n R / Ls2
Mm ~ m / R
R  Ls2 / R
Strings see space-time differently
Space-time a derived concept in String Theory
String length corresponds to a minimal length
7/19/2004
CERN HST 2004

22. String dualities
Five different string theories: embarrassment of riches
Turns out all 5 string theories are related through non-perturbative dualities (relations between seemingly different theories)
Found through supergravity and D-brane analysis: mapping the different states found in the different string theories
Includes an 11-dimensional strongly coupled theory, provisionally called M-theory, whose low-energy limit is 11-dimensional supergravity, but whose fundamental microscopic description is unknown, although membranes should play an important role
Provides a fully unified, consistent and beautiful picture
7/19/2004
CERN HST 2004

23. Strings and Cosmology
Recent observations have brought cosmological issues back to the foreground in String Theory
Singularity (Big Bang) resolution
Finding cosmological “vacua”
Understanding de Sitter space
Complicated because of
Time dependence of the background
Typically strongly coupled
Inflation corresponds to an effective de Sitter phase in the primordial universe
De Sitter space can be considered the cosmological equivalent of a black hole; one can define a de Sitter temperature and entropy
Note that AdS and dS space-time are “almost” the same
Gives some hope that now is a good time to address cosmological issues, but progress so far is slow
7/19/2004
CERN HST 2004

24. Strings Summary
String Theory corresponds to a very rich, extremely exciting, attractive theoretical structure which seems very promising in solving some long-standing mysteries: BH physics, quantum space-time, strongly coupled QCD and more
Not to mention the impact of String Theory in the area of Mathematics (geometry, topology) and Condensed Matter theory
Much remains to be done, from a formal point of view we still have not answered the basic question: “What is String or M-Theory”
Biggest problem from a physicist’s point of view: at the moment String Theory does not make a single falsifiable prediction
7/19/2004
CERN HST 2004

25. Credits and some useful links
Highly recommended: the popular science books “The Elegant Universe” and “The Fabric of the Cosmos” by Brian Greene
The Elegant Universe NOVA PBS website: includes links to multimedia and teacher resources
The “official” superstring website:
Another interesting website (prepared by the young string theorist Jan Troost):
My own Saturday Morning Physics lectures on String theory can be found at my homepage:
7/19/2004
CERN HST 2004