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Mar 2004

Mar 2008

Multi-loop structure of quantum supersymmetric gauge theories

In quantum field theory (QFT), all information about the dynamics of the quantised field is contained in the effective action. This is normally calculated perturbatively using Feynman diagrams, which are organised by their number of loops (cycles). Each loop gives a factor of Planck's constant ħ and can be thought of as a quantum correction. The QFTs that describe nature are gauge theories and their interactions are controlled by gauge symmetries. To calculate physical (gauge invariant) quantities, it is best if you can use a gauge covariant method. Such a method is the background field method, and its (manifestly covariant) application to multiloop diagrams was given by Kuzenko and McArthur in hep-th/0302205. Supersymmetric quantum field theories are a special class of QFTs that contain an extra symmetry that relates particles of different spin. This symmetry restricts the form of the effective action, these restrictions are called nonrenormalisation theorems. Superconformal QFTs can also be related to string theory through the AdS/CFT conjecture. This conjecture places further restrictions on the structure of the effective action. My thesis is to apply the methods of hep-th/0302205 to examine the multiloop structure of a variety of supersymmetric QFTs, and in doing so, testing various aspects of some nonrenormalisation theorems and the AdS/CFT conjecture.

On the theoretical level, the understanding of higher loop effective actions and the relationship of supersymmetric QFTs to string theory is still a very interesting and active area of research. Supersymmetric QFTs are some of the most well behaved and tractable QFTs at the theorists disposal, and thus form a perfect test bed for new ideas and methods. String theory is the most likely candidate for a quantum theory which includes gravity and the AdS/CFT conjecture is a two-way road that helps provide insight to both the string and field theory sides. On the more practical side, supersymmetric QFTs are the most popular candidate for“beyond the standard model” physics that is to be investigated at the recently commissioned large hadron collider (LHC) at CERN, Geneva. The techniques used and developed in this thesis can be applied to the more realistic supersymmetric QFTs to make predictions that can be tested at the LHC.

- Australia postgraduate award