SUPERSTRING THEORY:
PAST, PRESENT, AND FUTURE
John H. Schwarz
PITP Showcase Conference
May 13, 2005
I. 1968 - 1993
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.
A theory based on strings, rather than point-like
particles, can account for various features of the
strong nuclear force and the strongly interacting
particles (hadrons).
STRING DYNAMICS
For a point particle the motion makes the
invariant length of the world-line extremal.
S  m  ds
For a string the motion makes the invariant
area of the world-sheet extremal.
S  T  dA
The basic idea is that different quantum states
of the string correspond to the different types
of particles. So, there is a unique fundamental
object (namely, the string).
This string theory can be quantized, but this is
consistent only for 26 spacetime dimensions
(25 are spatial and 1 is time). The string
spectrum contains bosons only (no fermions).
Moreover, one of these bosons is a tachyon.
By adding fermionic coordinates to the worldsheet, another string theory that contains
fermions (as well as bosons) was constructed
in 1971 by Pierre Ramond, André Neveu, and
me. It requires 10 dimensions.
Its development led to supersymmetry, a new
type of symmetry that relates bosons and
fermions. Strings with this symmetry are called
superstrings.
In addition to the unrealistic dimension and the
tachyon, the string spectrum includes particles
that are massless, whereas all hadrons have
positive mass.
In the early 1970s a better theory of the strong
nuclear force, called quantum chromodynamics
(or QCD), was developed. As a result, string
theory fell out of favor.
UNIFICATION
One of the massless particles has precisely the
right properties to be the graviton -- the particle
responsible for the gravitational force.
In 1974 Joël Scherk and I proposed to use string
theory for the unification of all forces (including
gravity), rather than just the strong nuclear force.
Thus we stumbled upon a possible realization of
“Einstein's dream.”
THE SIZE OF STRINGS
When strings were supposed to describe
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!
This proposal had two big benefits:
All prior attempts to describe quantum
corrections to Einstein’s theory of gravity
assumed point particles. They gave nonsensical
infinite results (nonrenormalizable ultraviolet
divergences). String theory is UV finite.
Extra spatial dimensions can be compact in
string theory, where the geometry is determined
by the dynamics.
FIRST SUPERSTRING REVOLUTION
In 1984 Michael Green and I discovered that
superstring theory is free from certain expected
quantum inconsistencies, called anomalies, for
two special choices of the symmetry group:
SO(32) and E8 x E8
This raised hopes that a realistic theory can be
determined just by mathematical consistency.
The known symmetries fit nicely inside E8 .
MBG and JHS – Aspen 1984
FIVE THEORIES
Subsequently, two new superstring theories
with exactly these symmetries were
constructed by the Princeton string quartet.
By the time the dust settled, there seemed to
be five consistent superstring theories:
I, IIA, IIB, HE, HO
each of which requires ten dimensions.
Calabi-Yau Compactification
Certain six-dimensional manifolds, called CalabiYau spaces, solve the equations and give a
supersymmetric field theory in the remaining four
dimensions.
If one starts with the HE theory, and chooses the
right CY space, it is possible to come quite close
to achieving a realistic supersymmetric extension
of the Standard Model.
SPACE (or T) DUALITY
It was discovered in the late 1980s that different
geometries for the extra dimensions can be
physically equivalent!
For example, 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
II. 1994 - PRESENT
The period of discovery in the mid-1990s is
referred to as the
Second Superstring Revolution
Some of the most important contributors are
pictured on the next slide
Juan Maldacena
Joe Polchinski
Nathan Seiberg
Andrew Strominger
Cumrun Vafa
Edward Witten
STRENGTH (or S) DUALITY
This is another duality that relates a theory with
interaction strength g to one with strength 1/g.
Two examples are
I ↔ HO
and
IIB ↔ IIB.
Thus, since we know how to do calculations when
g is very small, we learn how these three theories
behave when g is very large.
M THEORY
What happens to the other two superstring
theories – IIA and HE – when g is large?
Answer: They grow an eleventh 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.
There’s just one theory!
Courtesy of John Pierre
BRANES
In addition to fundamental strings, superstring
theory predicts the existence of new objects,
called p-branes.
p is the number of spatial dimensions they
occupy. (For example, the fundamental string
is a 1-brane.)
Since the dimension of space is large (9 or
10), the allowed values of p can also be large.
BRANE WORLDS
Certain p-branes are called D-branes. They
have the property that strings can end on them.
One consequence is that quantum field theories
like the standard model can live on D-branes.
One intriguing possibility is that the observable
Universe is actually a set of 3-branes, which is
embedded in a space with 6 additional spatial
dimensions.
ADS/CFT DUALITY
In 1997 Maldacena proposed a new class of
dualities (or equivalences) – for example,
between a certain 4d QFT called N = 4 super
Yang-Mills theory and Type IIB superstring theory
in the 10d geometry AdS5 X S5.
The string theory is represented holographically
by the QFT, which is associated to the conformal
boundary of the 10d or 11d spacetime. Since the
QFT is conformally invariant (CFT), this is called
an AdS/CFT duality.
III. SOME REMAINING PROBLEMS
1. Find a complete and compelling formulation of
the theory
We do not yet have a compelling formulation
of the underlying theory. It may require some
principle that has not yet been understood.
The existence of space and time is probably an
emergent feature of specific solutions that is
not built into the underlying theory.
2. Understand empty space
The vacuum energy density, called dark energy,
is observed to be about 70% of the total energy
of the present Universe. It causes the expansion
of the Universe to accelerate.
This energy density is only about 10-122 when
expressed in Planck units. Anthropic explanation:
If it were much larger, we wouldn’t be here. Is
there another explanation? I hope so.
3. Explain elementary particle physics
Superstring theory may be unique, but its
equations have very many solutions (or quantum
vacua). 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?
4. Understand the role of supersymmetry
Supersymmetry requires that every particle
have a superpartner.
• What are their masses?
• Is the lightest superpartner (LSP) responsible for
dark matter?
• Can superpartners be made in collisions?
With Supersymmetry
Courtesy of The Particle Adventure
5. Understand spacetime and quantum
mechanics
What prevents “bad” spacetime singularities?
What ensures causality?
What are the microscopic quantum states that
are responsible for the entropy of black holes?
Is quantum mechanics exact?
What ensures that there is no loss of quantum
coherence for processes involving black holes?
6. Understand the origin and evolution of
the Universe
Trying to understand the whole Universe raises
yet more questions. How much of its origin,
structure, and evolution can be deduced from
first principles?
Observational cosmology is providing many facts
that need to be explained. Superstring
cosmology has recently become a very active
field of research.
7. Develop mathematical techniques and
concepts
String theory is up against the frontiers of several
branches of mathematics. Given our experience
to date, I expect that future developments will
require mathematical methods and concepts that
do not currently exist.
String theory is unifying disciplines as well as
forces and particles.