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Études on fuzzy geometry and cosmology
We investigate various aspects of noncommutative geometry and fuzzy field theory and their relations to string theory. In particular, we study the BPS and non-BPS solutions of the CJPN nonlinear sigma model on the noncommutative plane in some detail and show among other things that a class of its so...
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| Format: | Thesis |
| Language: | English |
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Department of Mathematics and Applied Mathematics
2016
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| _version_ | 1867613305067012096 |
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| access_status_str | Open Access |
| author | Murugan, Jeffrey |
| author2 | Ellis, George F R |
| author_browse | Ellis, George F R Murugan, Jeffrey |
| author_facet | Ellis, George F R Murugan, Jeffrey |
| author_sort | Murugan, Jeffrey |
| collection | Thesis |
| description | We investigate various aspects of noncommutative geometry and fuzzy field theory and their relations to string theory. In particular, we study the BPS and non-BPS solutions of the CJPN nonlinear sigma model on the noncommutative plane in some detail and show among other things that a class of its solitonic excitations may be built from bound states of noncommutative scalar solitons. We then go on to construct a fuzzy extension of the semilocal SU(N)a x U(l)L Yang-Mills-Riggs model. We find that not only does this noncommutative model support a large class of BPS vortex solutions but, unlike in the commutative model, these are exact solutions of the BPS equations. We also study the large coupling limit of the semilocal model and demonstrate conclusively the metamorphosis of the semilocal vortex to an appropriate degree instanton of the fuzzy CJPN model. In the second part of this work, we study the perpendicular intersection of Dl- and D7-branes in type liB string theory and the fuzzy 6-sphere that resolves the singularity of the intersection. We demonstrate the equivalence of the D7 and dual D-string descriptions by computing the energy, charge and radial profiles of the solution in each description. We conclude the thesis with a foray into cosmology by constructing a realisation of a recently proposed singularity-free inflating universe. We discuss the basic characteristics of this model and show that none are at odds with current observations. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/19023 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:34:00.978Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2016 |
| publishDateRange | 2016 |
| publishDateSort | 2016 |
| publisher | Department of Mathematics and Applied Mathematics |
| publisherStr | Department of Mathematics and Applied Mathematics |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/19023 Études on fuzzy geometry and cosmology Murugan, Jeffrey Ellis, George F R Applied Mathematics We investigate various aspects of noncommutative geometry and fuzzy field theory and their relations to string theory. In particular, we study the BPS and non-BPS solutions of the CJPN nonlinear sigma model on the noncommutative plane in some detail and show among other things that a class of its solitonic excitations may be built from bound states of noncommutative scalar solitons. We then go on to construct a fuzzy extension of the semilocal SU(N)a x U(l)L Yang-Mills-Riggs model. We find that not only does this noncommutative model support a large class of BPS vortex solutions but, unlike in the commutative model, these are exact solutions of the BPS equations. We also study the large coupling limit of the semilocal model and demonstrate conclusively the metamorphosis of the semilocal vortex to an appropriate degree instanton of the fuzzy CJPN model. In the second part of this work, we study the perpendicular intersection of Dl- and D7-branes in type liB string theory and the fuzzy 6-sphere that resolves the singularity of the intersection. We demonstrate the equivalence of the D7 and dual D-string descriptions by computing the energy, charge and radial profiles of the solution in each description. We conclude the thesis with a foray into cosmology by constructing a realisation of a recently proposed singularity-free inflating universe. We discuss the basic characteristics of this model and show that none are at odds with current observations. 2016-04-20T14:08:39Z 2016-04-20T14:08:39Z 2007 Doctoral Thesis Doctoral PhD http://hdl.handle.net/11427/19023 eng application/pdf Department of Mathematics and Applied Mathematics Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Murugan, Jeffrey Études on fuzzy geometry and cosmology |
| thesis_degree_str | Doctoral |
| title | Études on fuzzy geometry and cosmology |
| title_full | Études on fuzzy geometry and cosmology |
| title_fullStr | Études on fuzzy geometry and cosmology |
| title_full_unstemmed | Études on fuzzy geometry and cosmology |
| title_short | Études on fuzzy geometry and cosmology |
| title_sort | etudes on fuzzy geometry and cosmology |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/19023 |
| work_keys_str_mv | AT muruganjeffrey etudesonfuzzygeometryandcosmology |