STRING THEORY: CHALLENGES AND PROSPECTS

1. STRING THEORY:
CHALLENGES AND PROSPECTS
John H. Schwarz
October 2008

2. OUTLINE
I. What is string theory?
II. Challenges and Prospects

3. I. What is String Theory?
String theory arose in the late 1960s in an
attempt to understand the strong nuclear
force. This is the force that holds neutrons
and protons together inside the nucleus.
The theory must incorporate relativity and
quantum mechanics. If the fundamental
objects in the theory are loops or line
segments, called strings, rather than point-
like particles, it can account for features of
the strong nuclear force.

4. The basic idea is that different motions of
the string correspond to different types of
particles. So, string theory has a unique
fundamental object (namely, the string).
The original string theory (1968-69), called
the bosonic string theory, has several
fatal shortcomings. A much better one,
superstring theory (1971), overcomes
these problems.

5. BOSONIC STRING THEORY
• This theory describes bosons but not
fermions. These are the two basic classes
of particles in quantum theories.
• Consistency requires 26 dimensions (25 of
them are spatial and 1 is time).
• It has various other mathematical and
physical shortcomings, but it serves as a
good warm-up exercise.

6. SUPERSTRING THEORY
Another string theory that contains both
fermions and bosons was introduced in
1971 by Ramond, Neveu, and me. It
requires 10 dimensions (9 + 1).
Its development led to the discovery of
supersymmetry, a symmetry that relates
bosons and fermions. Strings with this
symmetry are called superstrings.

7. UNIFICATION
Both string theories contain massless
particles. One of them has just the right
properties to be the graviton -- the particle
responsible for the gravitational force.
In 1974 Scherk and I proposed using
string theory for unification of all forces
(including gravity).

8. EINSTEIN’S DREAM
A unified theory was Einstein’s focus in his later
years. However, the approach he pursued involved
trying to combine only electromagnetism and
gravitation (general relativity).
The nuclear forces were not yet understood, and
Einstein was uneasy with quantum mechanics,
even though he was one of its founders. So his
efforts were doomed from the outset.

9. THE SIZE OF STRINGS
When strings were supposed to describe
strongly interacting nuclear particles (hadrons)
their typical size needed to be
L ~ 10-13 cm
To describe gravity it needs to be roughly equal
to the Planck length
L ~ [ hG/c3 ]1/2 ~ 10-33 cm
Smaller by 20 orders of magnitude!

10. Advantages of String Theory
for Unification:
• Quantum corrections to Einstein’s theory of
gravity are infinite in point-particle theories. In
contrast, string theory gives finite results.
• The extra spatial dimensions can curl up and
become very small in a gravity theory, where
the geometry of space and time is determined
by the dynamics.

11. FIVE THEORIES
Following various breakthroughs in 1984, we
had five consistent superstring theories:
Type I, Type IIA, Type IIB,
Heterotic: HE and HO
Each of these is unique (without any free
parameters) and requires ten dimensions.

12. DUALITIES
String theory has many surprising truths.
One of them is that different geometries
for the extra dimensions can be physically
equivalent! This is called T duality.
e.g., a circle of radius R can be equivalent
to a circle of radius L2/R, where L is the
string length scale. Two such cases are
HE ↔ HO and IIA ↔ IIB

13. S DUALITY
Another surprising discovery is S duality. It
relates a theory with an interaction strength g to
another one with interaction strength g’ = 1/g.
Two examples are
I ↔ HO and IIB ↔ IIB.
Thus, since we know how to compute physical
quantities when g is very small, we learn how
these three theories behave when g is very
large.

14. M-THEORY
What happens to the other two theories
(IIA and HE) when g is large?
Answer: They grow an 11th dimension of
size gL. This new dimension is a circle in
the IIA case and a line interval in the HE
case.
Taken together with the dualities, this
implies that the five superstring theories
are actually different facets of a unique
underlying theory.

15. There’s just one theory!
Courtesy of John Pierre

16. In addition to fundamental strings, superstring
theory predicts the existence of objects with p
spatial dimensions, called p-branes. (The
fundamental string is a 1-brane.)
The values of p that can occur depend on the
theory. Since the dimension of space is large
(9 or 10), the allowed values of p can also be
large. For example, M-theory admits a 2-brane
and a 5-brane.
BRANES

17. BRANE WORLDS
Certain p-branes are called D-branes. They
have the property that fundamental strings can
end on them. One consequence is that quantum
field theories, like the standard model, can live
on these D-branes.
In this setup elementary particles and all forces
except gravity are restricted to the branes, while
gravity acts in all ten dimensions.

18. II. CHALLENGES AND
PROSPECTS

19. 1. Explain Particle Physics
The underlying theory is unique, but its
equations have very many solutions. One
of them should describe the microscopic
quantum world of particle physics.
Can we find it? Is it picked out by some
beautiful principle, or is it just randomly
chosen by our corner of the Universe?

20. Facts to Explain
• Four-Dimensional Spacetime
• Yang--Mills Quantum Field Theory with
SU(3) X SU(2) X U(1) gauge symmetry.
• Three families of quarks and leptons.
• The SU(2) X U(1) symmetry is broken to
the electromagnetic U(1) symmetry by
the Higgs mechanism. This gives mass
to the quarks and leptons.

21. 2. Understand the Role of
Supersymmetry
Supersymmetry, which is an essential
feature of superstring theory, implies that
every particle has a superpartner.
• What are their masses?
• Is the LSP responsible for dark matter?
• Can superpartners be made in collisions?
• How is supersymmetry broken?

22. With Supersymmetry
Courtesy of The Particle Adventure

23. 7 + 7 TeV proton – proton collider

24. Detectors

25. 3. Cosmology: Origin and
Evolution of the Universe
Trying to understand the whole Universe
raises similar sorts of questions. How
much of its origin, structure, and evolution
can be deduced from first principles?
Superstring cosmology has become a very
active field of research.

27. 4. Understand Empty Space
Empty space (or the “vacuum”) contains a
mysterious substance called dark energy.
It accounts for about 70% of the total
energy of the Universe, and it causes the
expansion of the Universe to accelerate.
The density of this energy is 10^(-120),
when expressed in Planck units. How can
we understand this number?

28. 5. Find a Compelling
Formulation of the Theory
We do not have a compelling formulation
of the complete underlying theory. This
may require some new principle.
The existence of space and time is likely
to be an emergent feature of specific
solutions that is not built into the
underlying theory.

29. Spinoffs
• Mathematical discoveries
• Properties of high temperature
nuclear matter
• Condensed matter systems, such as
high temperature superconductors

30. Conclusions
• String theory unifies disciplines as well
as forces and particles.
• We have been exploring string theory
for 40 years, but there is a long way to
go.
• I find it amazing that we might be able
to answer such basic questions.