Supersymmetriska kvantfältteorier i fem dimensioner
Tidsperiod: 2013-01-01 till 2014-12-31
Projektledare: Johan Källén
Budget: 2 100 000 SEK
In this research project we will study theoretical and mathematical aspects of quantum field theories. Quantum field theory is a theoretical framework used to describe e.g. elementary particles and their interactions. A solid understanding of quantum field theories is therefore important in order to understand basic aspects of Nature. There are still many aspects of the theory which is not well understood. For example, in general it is very difficult to obtain exact results, often one has to rely on perturbative expansions around a small coupling constant. However, in many situations in Nature the theory is strongly coupled and the perturbative expansion breaks down. In this research project we will study a technique which allows for calculations at strong coupling. The technique is called "localization of the path integral", and we will apply it to supersymmetric quantum field theories five dimensions. Such theories can hardly be used for a realistic model of Nature, we are not there yet. Instead they should be looked at as a theoretical laboratory in which we can learn about elusive aspects of quantum field theories in simplified situations, and such a knowledge might eventually lead to a better understanding of Nature. Specifically, I will try to understand the contributions from instantons in supersymmetric Yang-Mills theory on the five-sphere. In addition, these type of quantum field theories have interesting applications in pure mathematics which I am going to explore.