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

dsmS

dATS

For a point particle the motion makes the invariant length of the world-line extremal.

For a string the motion makes the invariant area of the world-sheet extremal.

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 world-

sheet, 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!

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.

This proposal had two big benefits:

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 Calabi-Yau 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

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.

BRANES

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?

Trying to understand the whole Universe raises yet more questions. How much of its origin, structure, and evolution can be deduced from first principles?

6. Understand the origin and evolution of the Universe

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.