3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item The simplest gauge-string duality(2015) Nkumane, Lwazi KhethukuthulaThe gauge/gravity correspondence is a conjectured exact duality between quantum eld theories and theories of quantum gravity. A very simple gauge/string duality, claims an equivalence between the Gaussian matrix model and the topological A-model string theory on P1. In this dissertation we study this duality, proposing concrete operators in the matrix model that are dual to gravitational descendants of the puncture operator of the topological string theory. We test our proposal by showing that a large number of matrix model correlators are in complete agreement with correlators in the dual topological string theory. Contact term interactions, as proposed by Gopakumar and Pius, play an interesting and non-trivial role in the duality.Item Vector-like description of SU (2) matrix-valued quantum field theories(2015-05) Johnson, Celeste IreneThe AdS/CFT correspondence asserts a duality between non-Abelian gauge theories and quantum theories of gravity, established by the value of the gauge coupling . Gerard t'Hooft found that the large N0 limit in non-Abelian Yang-Mills gauge theories results in a planar diagram simpli cation of the topological expansion. In this dissertation, SU(2) gauge theories are written in terms of vector models (making use of collective eld theory to obtain an expression for the Jacobian), a saddle point analysis is performed, and the large N limit taken. Initially this procedure is done for gauge theories dimensionally reduced on T4 and R T3, and then attempted for the full eld theory (without dimensional reduction). In each case this results in an expression for the non-perturbative propagator. A nite volume must be imposed to obtain a gap equation for the full eld theory; directives for possible solutions to this di culty are discussed.Item Instantons in D=5 super-Yang-Mills theory(2014-07-07) Tahiridimbisoa, Nirina Maurice HasinaOne of the key goals of string theory is to provide a uni cation of general relativity and quantum eld theory. In the pursuit of this goal it has become clear that the di erent string theories that have been discovered so far are all in fact, partial descriptions of a single theory. At strong coupling a new theory, called M-theory, is the correct description. M-theory includes gravitons, M2-branes and M5-branes. Up to now, the correct description of the M5-brane is outstanding. In this project some proposals for this theory are studied. In particular, there is a proposal that D=5 maximally supersymmetric Yang-Mills theory can be used to provide a description of the world volume physics of the M5-brane. According to this proposal, instantons in D=5 maximally supersymmetric Yang-Mills theory are graviton excitations of the M theory. In this M.Sc dissertation the instanton solutions of D=5 maximally supersymmetric Yang-Mills theory are explored, with the goal of testing the above proposal. The dissertation begins with a review of the uses of instantons in quantum mechanics. In particular, instantons are used to account for tunneling e ects within a path integral approach to quantum mechanics. The lifting of ground state degeneracies as well as the estimation of the lifetime of unstable states using instantons is developed. The quantization of gauge theories is reviewed in detail. The relevance of instantons for a semi-classical study of Yang-Mills theory is explained. Finally, the relevance of instantons for D = 5 maximally supersymmetric Yang-Mills theory is considered.