Localization Of Gravitino And Gauge Fields On Braneworlds

The extra dimension and braneworld theories have been brought into sharp focus because they provide new approaches to address some outstanding issues such as the gauge hierarchy problem and the cosmological constant problem. In the braneworld scenarios, the localization mechanisms of bulk fields on a brane are very important, which can realize the construction of the Standard Model of four-dimensional particles and also provide a guidance on experiments in future. Furthermore, the investigation of dark matters is one of frontier subjects, while the gravitino as the supersymmetric partner of graviton can describe some properties of dark matters and be regarded as one of dark matters. In this paper we will mainly investigate the localization and resonances of the five-dimensional gravitino and gauge (Kalb-Ramond(KR) and vector) fields on thin and thick branes.Firstly, we review briefly the development history of the extra dimensions and brane-world theories, and introduce the KK theory, the Arkani-Hamed-Dimopoulos-Dvali(ADD), and the Randall-Sundram (RS) models as well as the scalar tensor model. The thin brane models (ADD and RS) were mainly tried to solve the gauge hierarchy problem, and at the same time opened the prelude to the development of the braneworld. However, the thickness of brane in these thin brane models is ignored, and the thin branes are merely a ideal in the mathematics. Therefore, the thick brane theory were built up and then devel-oped further as considered the thickness of brane. In the thick brane theory, the energy density of brane constructed by introducing scalar fields can be spread along the extra dimensions. Since the form of scalar fields are not explicitly limited, there are various solutions of thick branes.Secondly, we investigate the localization of the five-dimensional gravitino field on thin branes with S1/Z2 extra dimension (RS and the scalar tensor models). It has been shown that:(i) for the RS model, there are the massless chiral modes on branes and the massive KK chiral modes. And from the physical coordinate, there are several lower massive KK chiral modes near the TeV brane, (ii) for the scalar tensor model (considering two brane solutions), the localization of the massless chiral modes are determined by the parameter A. Since the KK mass spectrum and the localization property are different, these two brane solutions are not physically equivalent.Then, in the third chapter we study the localization of the KR field on the symmetric and asymmetric thick brane (three parameters brane solution) through introducing the coupling f(φ(z))= e(-7-2p)A(z) (p< -9/2). It shows that the effective potential of KK modes is a volcano-like one, and there are the massless KR field on the brane and several massive KK resonances. In particular, we use the relative probability and transfer matrix methods numerically to solve resonances for the symmetric thick brane, while firstly in this literature useing the transfer matrix method for the asymmetric case. Furthermore, when the parameter s is limited, the number of resonances will be increased with increasing the thickness of brane (λ) and decreasing the coupling parameter (p).Finally, the localization of the interactive U(1) gauge field (also regard as the changed massive vector field) on the symmetric and asymmetric degenerated Ⅰ and Ⅱ Bloch thick branes are studied further. Decomposing the U(1) gauge field in the five-dimensional spacetime into one vector degree and two scalar degrees, we obtain the massless vector field on Bloch branes and several massive KK resonances. It has been shown that there are two massless scalar modes and they are dependent with each other, while the massive scalar modes are decoupled. Furthermore, the effective potential of the scalar degrees is the infinite well. Therefore, there are only one massless scalar mode and two kinds of the massive scalar modes.