ELEMENTARY PARTICLE PHYSICS

In order to understand the context of this project, the Standard Model of particle physics and the peculiar nature of the strong interactions need to be explained. The Standard Model describes all known elementary particles and interactions, except the gravitational interaction. Thus it is a very general and successful description of nature, but it is know to fail at very high energies and when confronted with astrophysical observations.

These observations have revealed the presence of a large amount of so-called Dark Matter that does not consist of the constituents of the Standard Model. In fact only a small fraction of the total amount of matter in the universe consists of Standard Model particles.

In addition there are theoretical problems with the description of the Standard Model like the Hierarchy Problem and there are so far unexplained patterns in its contents. All of these shortcomings have motivated a long time search for an extension of the Standard Model.

Supersymmetry provides one of the most prominent guiding principles for such an extension. It is a symmetry that connects two different classes of particles: the bosons, like the exchange particles of the forces and the Higgs particle, are related to the fermions, the quarks and leptons like the electron. The investigation of the non-perturbative sector of supersymmetric theories requires numerical simulations which are done in this project.

Apart from the search for its extensions, there has also been a large scientific effort to understand the physics of the Standard Model itself. Of the three different forces of the Standard Model, only the electromagetic force can be observed at the scales of our everyday life. The interaction range of the weak force is limited by the mass of its exchange particles. In case of the strong force, the range is limited by the interaction strength due to a phenomenon called confinement. At low energies and low temperatures, the force binds the elementary particles such that with respect to its charges only neutral bound states can exist.

While the other interactions of the Standard Model can be investigated using perturbative expansion techniques, the confinement is still out of the reach of an analytical understanding. However, numerical lattice simulations on large scale computing facilities have provided insights into the properties of the confined theory. Moreover, certain supersymmetric versions of strongly interacting theories allow for analytical investigations of non-perturbative phenomena.

In order to connect these result with more realistic theories, complementary general methods are required. The second aim of the numerical lattice simulations of this project is to offer such a tool that allows to investigate how the insights of the strongly interacting supersymmetric theories can be generalized.

The essential basic non-perturbative properties of supersymmetric Yang-Mills theory investigated in this project are the bound state mass spectrum and the phase transitions. The low energy bound state particles have been found to form supersymmetry multiplets, which shows that the symmetry remains unbroken at low energies. The deconfinement transition at which the confining nature of the theory breaks down due to thermal fluctuations and the critical temperature for fermion condensation have been identified and found to be identical within the numerical accuracy. Currently we are extending the project towards more general supersymmetric gauge theories.