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I would like to thank my adviser Prof. Tonnis ter Veldhuis, Associate Professor of Physics at Macalester College.

Abstract

The dynamics of the center of mass motion of a soliton embedded in a curved (1+1)-dimensional Anti-de-Sitter (AdS) space as well as a finite number of its low frequency excitations is modeled using the method of non-linear realizations. The variations of the field representing the center of mass coordinate and of the time coordinate under isometry group transformations are determined by use of the coset method. The covariantly transforming Maurer-Cartan one forms are constructed as the building blocks from which an invariant Lagrangian is constructed. This Lagrangian can be expanded in terms of a scale which physically represents the inverse width of the soliton. Considering the simplest form of the invariant Lagrangian by keeping only the universal lowest order term in the expansion, the classical Euler-Lagrange equations of motion are obtained from the action by the least action principle. The solution of the equation of motion describes the motion of a point particle in AdS space, as expected. The Noether method is used to determine the conserved charges associated with the isometries of the model. These conserved charges are the equivalents of energy and momentum in flat Minkowski space. The dual, conformally invariant model is determined, and the relation between the two models is studied as a first attempt to elucidate the AdS-CFT correspondence for this system. A supersymmetric extension of the model is constructed by the introduction of additional Grassmann coordinates.

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