Études on fuzzy geometry and cosmology

 

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dc.contributor.advisor Ellis, George F R en_ZA
dc.contributor.author Murugan, Jeffrey en_ZA
dc.date.accessioned 2016-04-20T14:08:39Z
dc.date.available 2016-04-20T14:08:39Z
dc.date.issued 2007 en_ZA
dc.identifier.citation Murugan, J. 2007. Études on fuzzy geometry and cosmology. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/19023
dc.description.abstract 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. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Applied Mathematics en_ZA
dc.title Études on fuzzy geometry and cosmology en_ZA
dc.type Doctoral Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Mathematics and Applied Mathematics en_ZA
dc.type.qualificationlevel Doctoral
dc.type.qualificationname PhD en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Murugan, J. (2007). <i>Études on fuzzy geometry and cosmology</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/19023 en_ZA
dc.identifier.chicagocitation Murugan, Jeffrey. <i>"Études on fuzzy geometry and cosmology."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2007. http://hdl.handle.net/11427/19023 en_ZA
dc.identifier.vancouvercitation Murugan J. Études on fuzzy geometry and cosmology. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2007 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/19023 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Murugan, Jeffrey AB - 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. DA - 2007 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2007 T1 - Études on fuzzy geometry and cosmology TI - Études on fuzzy geometry and cosmology UR - http://hdl.handle.net/11427/19023 ER - en_ZA


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