# The Spectrum of Supersymmetric Yang-Mills Theory

The physics of elementary particles has shown that the known matter is composed of a small number of building blocks. Among them there are the so-called quarks and leptons. The „Standard Model“ of particle physics successfully describes these particles and the forces, which act between them, and is in best agreement with the experimental results.

Nevertheless, there are reasons for believing that there are physical phenomena beyond the Standard Model. These reasons are based on observations (e. g. neutrino oscillations, evidence for dark matter) and on unsatisfactory theoretical properties of the Standard Model, among other things a large number of free parameters. Many of the attempts to extend the Standard Model are based on the concept of supersymmetry. Supersymmetry generalises the conventional concept of symmetry in physics in a quantum theoretical manner. It relates bosonic to fermionic particles and has the potential to fix some of the problematic aspects of the Standard Model.

In a joint project of scientists of the Universitiy of Münster, the University of Frankfurt, and of DESY, Hamburg, researchers investigate the properties of the N = 1 supersymmetric Yang-Mills theory, a theory which has supersymmetry and is part of many models for the physics beyond the Standard Model. On the one hand this theory describes gluons, the mediators of the strong forces of elementary particles. On the other hand, supersymmetry requires that the gluons be paired with their superpartners, the gluinos, which are fermions with spin 1/2. The complex self-interaction of the gluons is extended by the interaction between gluons and gluinos. Of particular interest is the spectrum of the lightest particles, which are described by this theory. It consists of bound states of gluons and gluinos, which are expected to be arranged in supersymmetric groups of particles, called supermultiplets. There are also a number of other questions about this theory, which one wants to explore. A method to investigate such questions that cannot be solved with pencil and paper, is the numerical simulation of the theory with the help of computers. To this end space and time need to be discretised and replaced by a four-dimensional lattice. In order to get precise enough results, the number of lattice points has to be sufficiently large and one has to generate a large number of configurations representing states of the model. Therefore the simulations need to be carried out on the GCS-Supercomputer JUQUEEN in Jülich. They are supplemented by theoretical calculations.

Thanks to the simulations and to the analysis carried out with special programs written by the researchers, the scientists were able to obtain results on the masses of the lightest particles, on the forces between the fundamental charges and on other fundamental properties of the theory. They also examined the extent to which supersymmetry is violated by the discretisation of space and time. The achieved results are compatible with the existence of a supersymmetric continuum limit and the formation of supermultiplets.

The research on this subject will continue and it will aim at a further understanding of other aspects of the theory, e.g. its behaviour at high temperatures.

Copyright: © Westfälische Wilhelms-Universität Münster

*Figure: Results for the mass of a bound state of gluinos and gluons. In order to approach the supersymmetric limit the data are extrapolated to the limit of vanishing gluino mass (corresponding to m*

_{π}=0.)**Team: **

Georg Bergner (Johann Wolfgang Goethe-Universität Frankfurt am Main)

Pietro Giudice (Westfälische Wilhelms-Universität Münster)

István Montvay (Deutsches Elektronen-Synchrotron/DESY, Hamburg)

Gernot Münster (Westfälische Wilhelms-Universität Münster)

Umut D. Özugurel (Westfälische Wilhelms-Universität Münster)

Stefano Piemonte (Westfälische Wilhelms-Universität Münster)

Dirk Sandbrink (Westfälische Wilhelms-Universität Münster)

Prof. Dr. G. Münster

Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster

Wilhelm-Klemm-Str. 9, D-48149 Münster/Germany

e-mail: munsteg@uni-muenster.de