Today, theoretical physics is able to make predictions in the range of both the smallest experimentally resolvable and the largest observable distances that are in remarkably precise agreement with the observed data. On the one hand, there is the standard model of elementary particle physics, which is almost perfectly confirmed by all accelerator experiments. This model is a quantum field theory, i.e. it combines the basic principles of quantum theory (description of physical states by vectors of a Hilbert space) and the special theory of relativity (global Lorentz invariance). No deviation from the predictions of the (locally Lorentz-invariant) general theory of relativity could be observed in the range of large length scales.

Why string theory?

The biggest problem with both theories is their incompatibility. For example, in order to describe physical processes in the vicinity of spacetime singularities, it is essential to use a quantum theory of gravity. So far, however, all attempts to develop a point particle theory of gravity have failed due to the non-renormalizability of gravity. Thus, a unified theory of all fundamental physical interactions must violate one of our basic ideas.


A two-dimensional visualization of a Calabi-Yau-threefold


A two-dimensional visualization of a Calabi-Yau-threefold

Strings and compactification

String theory is able to unite the basic principles of quantum theory and general relativity. The assumption that is abandoned is that elementary particles are point-like. Instead, one-dimensionally extended objects capable of vibrating like strings (hence the name) are postulated. The observed particles then correspond to excited vibrational states of the strings. The resulting spectrum should not contain any tachyons (particles with negative mass squared), and the resulting low-energy quantum field theory must be anomaly-free. These requirements turn out to be extremely restrictive. They can be fulfilled, for example, by formulating the supersymmetric variant of the theory in a product space, where one factor is the (3+1)-dimensional Minkowski space, while the other factor is a so-called Calabi-Yau three manifold (a compact space of three complex, i.e. six real dimensions with very special properties).

Webpages, opens an external URL in a new window (homepage Harald Skarke), opens an external URL in a new window (database on Calabi-Yau manifolds)


H. Skarke, opens an external URL in a new window