In this thesis we consider the N=1 super Yang-Mills theory on S5 with a single hypermultiplet in the adjoint representation. We argue that there is a critical value of the hypermultiplet mass M=3/2r, where r is the radius of S5, for which the free energy vanishes, and we study the model in the proximity of this value. For large N we provide analytical results for the free energy and the eigenvalue density in the weak and strong coupling limits, and in one case we solve the saddle point equation using a technique introduced by Hoppe. We present numerical results to show where each approximation is justified, and to explore the regimes where the model cannot be solved analytically. Based on the numerical results, we argue that in most cases the behaviour of the model is better understood in terms of an effective coupling constant λ'=λM. For small M the model simplifies to one whose kernel is non-singular. This simplified model shows a peculiar peak structure in the eigenvalue distribution, with the number of peaks growing as the effective coupling is increased. We interpret this as a series of phase transitions as M approaches 3/2r.
| Identifer | oai:union.ndltd.org:UPSALLA1/oai:DiVA.org:uu-235752 |
| Date | January 2014 |
| Creators | Borla, Umberto |
| Publisher | Uppsala universitet, Teoretisk fysik |
| Source Sets | DiVA Archive at Upsalla University |
| Language | English |
| Detected Language | English |
| Type | Student thesis, info:eu-repo/semantics/bachelorThesis, text |
| Format | application/pdf |
| Rights | info:eu-repo/semantics/openAccess |
| Relation | FYSAST ; FYSMAS1022 |
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