Visão supersimétrica de modelos topológicos e branas em D=4 e D=5

• Ano de defesa: 2008
• Autor(a) principal: Nunes, Luciana Angelica da Silva
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Palavras-chave em Português: Supersimetria; Modelos topológicos
• Link de acesso: http://www.repositorio.ufc.br/handle/riufc/12776

The main line of this thesis is related to supersymmetric theories. To this main line we join a discussion about Kalb-Ramond field propagators in branes. Indeed, the antisymmetric fields are another conductor line of this work, appearing in almost all the topics. Initially, considering Dirac δ branes, which are typical in Dvali and Randall-Sundrum models, we show that a relationship which occurs between vectorial field propagators in D = 4 and D = 5 space-time dimensions, remains valid when we treat antisymmetric tensorial fields. Such result supports speculation about localization of tensorial fields in branes. Related to supersymmetric theories, our investigations are threefold: 1) topological models in D = 5, in the context of the so called pseudo-supersymmetry; 2) construction of a complete description of a N = 1 - D = 5 superspace, unprecedented in the literature, which we call intrinsical superspace, in order to make difference respect with pseudo-supersymmetry in D = 5; 3) description of the Aharanov-Casher effect in a supersymmetric theory in D = 4 with Lorentz breaking term. In the context of topological models, we carried out a D = 5 pseudo-supersymmetric extension of a term structurally analog to the Chern-Simons term, but involving only the Kalb-Ramond tensorial gauge field BMN = (Bmn,Bm5). We obtain a complete expansion for the super fields and prove in details the number of the degrees of freedom of the antisymmetric tensorial rank-2 eld in D = 5. Since we constructed the complete expansion of the Kalb-Ramond super field, we find the fermionic superpartner of the 5-dimensional topological term. On the other hand, since we consider unsatisfactory the present formalism in the literature which treat supersymmetric systems in (4+1) dimensions, particularly if we have in mind applications to brane models, we constructed a formalism for the N = 1 - D = 5 superspace. We find the generators and consequently, the supersymmetric covariant v derivatives and we show that exist an explicit dependence on the fifth coordinate. This result allows propagation in the extra dimension, which is not described in the pseudosupersymmetry formalism, since there are used the same 4D supersymmetric covariant derivatives. The Wess-Zumino model in five dimensions was written using the formalism of the intrinsical supersymmetry, as well as a vectorial super field, which allowed the construction of a manifestly supersymmetric gauge invariant theory in D = 5. Finally, in the context of a D = 4 supersymmetric theory, we used an ansatz in order to break the Lorentz symmetry, simply by imposing that determined field of the model is constant, although the supersymmetry is preserved. Besides, we add a Fayet-Illiopoulos term, which give us a potential and from the presence of this potential we write a new lagrangian which allows us to obtain the so called Aharonov-Casher effect in a supersymmetric theory with Lorentz breaking. It is worthwhile to mention four appendices, namely: convention and revision of spinors; differential forms for super fields; a detailed proof of existence of three degrees of freedom on-shell in D = 5 for the Kalb-Ramond field; and the deSitter algebra in the vectorial and spinorial SO(1, 4) representations.