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Dynamical Realization of the Brane world Scenario Using Topological Solitons

In this thesis we discuss how the brane world scenario can be realized dynamically within the field theoretical framework using topological solitons. As a playground we consider a bosonic sector of a (4+1)-dimensional supersymmetric gauge theory, which naturally supports soliton of co-dimension one, a domain wall. We first discuss separate localization of matter fields and gauge fields on the world-volume of the domain wall and then we present two explicit five-dimensional models, where both matter fields and gauge fields are localized together with minimal interactions. We show that matter fields localize in the adjoint representation of the non-Abelian gauge group and we calculate the effective interaction Lagrangian of these matter fields up to the second order in derivatives. We discuss similarities of our models with effective models describing pions in QCD and with D-branes from string theory.