The one-loop effective action for N = 2 and N = 4 supersymmetric Yang-Mills theories are computed to order F5; and F6 respectively by the use of heat kernel techniques in N = 1 superspace. The computations are carried out via the introduction of a new method for computing DeWitt-Seeley coefficients in the coincidence limit. To order F5, the bosonic components of both N = 2 and N = 4 supersymmetric Yang-Mills theories are extracted and compared with the existing literature. For N = 4 super Yang-Mills theories the F5 terms are found to be consistent with the non-Abelian Born-Infeld action computed to this order by superstring methods and various other means of computing deformations of supersymmetric Yang-Mills theory. The result proved to be the final piece of a puzzle, leaving little doubt that there exists a unique deformation of maximally symmetric super Yang-Mills theories at this order. The F6 terms will be of importance for comparison with superstring calculations, including direct tests of the AdS/CFT conjecture. The bosonic components of N = 2 supersymmetric Yang-Mills are also shown to be consistent with existing literature, and will be of importance for testing of generalizations of the AdS/CFT conjecture.
| Identifer | oai:union.ndltd.org:ADTP/221442 |
| Date | January 2007 |
| Creators | Grasso, Darren Trevor |
| Publisher | University of Western Australia. School of Physics |
| Source Sets | Australiasian Digital Theses Program |
| Language | English |
| Detected Language | English |
| Rights | Copyright Darren Trevor Grasso, http://www.itpo.uwa.edu.au/UWA-Computer-And-Software-Use-Regulations.html |
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