String Theory (switch to Swedish)

(Marcus Berg, Jürgen Fuchs)

The established Standard Model of particle physics is a quantum theory, where all matter is built out of quarks (like in the proton) and leptons (like electrons), point particles of exactly zero radius. At first sight, this seems strange: why couldn't the elementary building blocks be extended objects of nonzero size? In fact, many physicists in the past attempted to create such theories and failed, like a prescient paper from 1962 by Paul Dirac, one of the founders of quantum theory. In modern physics, string theory is the only known example of a microscopic theory of extended objects that seems to be free from internal problems.

A perhaps even deeper question about the world we live in is: why are there three spatial dimensions: height, length and width? Unlike the question about nonzero size, this seems like a stupid question at first sight: what else could there be? But extra dimensions of space is an old idea, one of the first to think about this was a Swedish physicist, who got Einstein interested in the idea. What is amazing in string theory is that the possible existence of new spatial dimensions is connected to the hypothesis of nonzero size of the elementary objects. This follows from a mathematical calculation that can be performed in a Master's level physics course.

In the 1990s, it was realized that the elementary objects of string theory can look not only like strings (imagine a tiny, tiny guitar string), but there are also "membranes" (like drumskins, or higher-dimensional analogs thereof). These membranes are simply the places where strings can end. In a mechanics course, we might study oscillations of a guitar string, and the mathematical description of this is a differential equation with a so-called "Dirichlet condition" where the string is stuck. So these elementary membranes are called Dirichlet-branes or D-branes for short.

Now, the D-brane can vibrate like a drumskin, and calculating the vibrations of the D-brane we find matter particles like quarks and leptons that we set out to describe, but also other particles like the one labelled in the figure on the right. These are found in the last column of the "periodic table" of particles, the column that produces forces, and one example is the gluon particle, that provides the strong nuclear force that keeps the proton together. So D-branes capture all the known aspects of particle physics, and more: the blue wiggly lines and the black tube in the figure correspond to ripples in a gravitational field. In fact, as you may have noticed, this picture expresses aspects of particle physics as geometry, which gives hope to connect this theory to Einstein's successful geometric theory of gravitation (see "Research").

For D-branes of at least three spatial dimensions, our universe can be located on the D-brane, like the red one in the figure. Particle processes are naturally confined to this universe, but there can be another "universe" (blue) separated from us in the extra dimensions by a distance φ, and the two D-branes interact with gravity-like forces. The diagram in the figure represents a specific mathematical expression for a probability that vibrations of the D-brane interact in a given way, analogous to a Feynman diagram in quantum theory. At its simplest level, string theory is merely a set of rules for calculating such probabilities.

Much of the effort to find experimental tests of string theory use D-branes. In 2003, the first stable string models were constructed that contain the Standard Model and much beyond it, see for example this article. Part of the focus on string theory research at KaU is: what do these string models say about cosmology and particle physics? And since this is all so new, what mathematical tools (like conformal field theory, see "Research") do we need to develop to understand it better?

D-branes were also the tools which which the so-called AdS/CFT correspondence was discovered in 1997, by Juan Maldacena and others. This correspondence is a powerful relation between a strongly interacting (i.e. complicated) particle theory on the one side, to a weakly interacting (i.e. relatively simple) string theory with gravity, but where the latter has one more dimension. The hope is that this strong-weak "dictionary" will provide new methods to calculate aspects of the strong nuclear force, and it has also lead to new models in the physics of materials. There is a useful general article about the correspondence by Maldacena and one of his co-discoverers.

Finally, since you made it all the way down here, we can treat you to an informal story of how string theory was indirectly useful for the experimental search for a Higgs particle, in this blog entry.