String Theory Research at UC Berkeley

In classical general relativity there are almost no restrictions on spacetime and its matter content. Einstein's equations are perfectly consistent in any number of dimensions, for open as well as closed universes, for universes with a positive cosmological constant (dark energy) and for universes with a zero or negative cosmological constant. The goal of research in string theory is to restrict the structure of spacetime and its matter content by combining gravity with the principles of quantum mechanics. We are learning about fundamentally new principles that seem to be relevant at short distances. The ultimate goal is to find a clear picture that perhaps combines and extends all the bits and pieces and that singles out the correct model of particle theory and explains the mysteries of cosmology.

Here are some of the bits and pieces:

The holographic principle

In the 1970s theoretical investigations by Bekenstein and Hawking of the thermodynamic properties of black holes have led to the conclusions that A holographic tea pot
(A Holographic Tea Pot)
Image Credit & Copyright: E. Winfree, K. Fleischer, A. Barr et al. (Caltech)
See also: Astronomy Picture of 5/18/2003.

Entropy is related to the number of different configurations of a system, and the entropy of ordinary materials is usually proportional to their volume. The fact that the entropy is proportional to the area is very surprising. Following later ideas by 't Hooft, Susskind, Maldacena, Witten and Bousso, it became clear that this peculiar behavior is a general property of Quantum Gravity and not just black holes.
It reflects the fact that on a microscopic level there are many relations between different spacetime events. It also suggests that if there are independent fundamental degrees of freedom that describe quantum gravity they live on two dimensional surfaces and not the whole of space.
The name holographic is drawn from an analogy with a hologram, which can be broken to many pieces and yet every piece contains the information of the whole picture.
It is an open problem how exactly quantum gravity manages to describe a three dimensional geometry using two dimensional degrees of freedom.

We can get clues about quantum gravity by thinking about places where classical general relativity breaks down. Such a place is called a singularity.
General relativity breaks down when there is some discontinuity in spacetime. Two important examples are
  • The center of black holes and,
  • The Big Bang.
It is unknown how to describe these spacelike singularities.
But there are other simpler kinds of singularities that string theory does know how to describe!
The Big Bang and black hole singularities are of the spacelike type. This means that they extend throughout space and occur at a single point in time.
(It is obvious that the Big Bang is a point in time. But why is the center of a black hole spacelike? This seems counter intuitive but it is true! The singularity of a black hole is the end of time for an observer that falls into the black hole.)
The singularities that string theory can describe at the moment are certain simple timelike singularities. Such singularities exist at all times and are localized in space.
It turns out that there is a surprising connection between gauge theories, such as those that appear in particle theory, and the string theoretic description of such singularities. This fact is very important in various models that attempt to reproduce the standard model of particle theory.
Penrose diagram of a black hole and its singularity

Geometry of extra dimensions
String theory models predict ten spacetime dimensions (nine space dimensions and one time). M-theory, which is a certain strongly-coupled limit of string theory, predicts eleven spacetime dimensions. The extra dimensions (six in string theory and seven in M-theory) are believed to be very small. The geometrical shape of these dimensions and the singularities in these extra dimensions can explain the various types of particles in nature.
Although many important details, such as supersymmetry breaking, are unknown, the study of the possible shapes of the extra dimensions is important. This research field involves tools from advanced geometry and group theory.

Field theories in higher dimensions
String theory predicts the existence of consistent quantum field theories in spacetime dimensions higher than four. In particular there are very mysterious theories in six dimensions. Those theories are unlike any ordinary known quantum field theory. They do not have a coupling constant, and they have string-like objects that are simultaneously electrically and magnetically charged. A better understanding of such theories will shed new light on nonperturbative effects (i.e., effects that cannot be Taylor expanded in the coupling constant and are therefore very hard to analyze) in four dimensional gauge theories.
Extra dimensions

Nonlocal field theories and noncommutative geometry
The requirement of local interactions is usually assumed as a principle of quantum field theory. It is, however, possible to drop this requirement and, at least in theory, define a nonlocal quantum field theory.
It turns out that such nonlocal quantum field theories naturally arise in theoretical string theory. In such theories the nonlocal interactions are explained by fundamental strings that can stretch between different points of spacetime.
These ideas are also related to the notion of noncommutative geometry. This is an abstract modification of analytic geometry in which coordinates are no longer ordinary numbers. Instead, they are taken to be abstract variables that do not commute. In noncommutative geometry the rules are very strange. For example, multiplying x by y is not the same as multiplying y by x. The order is important!
The existence of such theories changes our fundamental notion of spacetime. It is also related to another important concept of particle and string theory: Supersymmetry.
Nonlocal interactions

Last updated on October 23, 2004.
Please send comments on this webpage to Ori Ganor.