Bulk Matter Fields And Their Kk Modes On Brane Worlds

The brane world theory has received more and more attention, as it opened up new avenues to explain some questions, such as the hierarchy problem, and the cosmological constant problem. In this thesis, we focus on the matter fields and their KK modes in brane world, and the aim is to find a way to theoretically prove the brane world theory, by analyzing the KK modes of matter fields.In the development of the brane world theory, there are two types of brane models proposed, i.e., the thin brane and the thick brane models. The famous thin brane models are the ADD and the RS. These two theories mainly tried to solve the hierarchy problem, and they open the prelude of the brane theory. However, the thickness of the brane was ignored in these theories, and thin brane was merely a mathematical idea. So the thick brane theory was built up. In the thick brane theory, the energy of the system can spread along the extra dimension. And the thick brane is generated by a back-ground scalar field. Due to the freedom in choosing scalar potential, there are various solutions of thick branes.In the brane world theory, the particles in the Standard Model are supposed to be confined on the brane, while gravity can propagate freely outside of the brane. Thus, we need a mechanism to localize the matter fields naturally, which can also make the brane world be consistent with the actual world. And this is to be sure for a realized brane world model. In this thesis, we study one of the mechanisms that can confine the matter fields on the brane, namely, the localization.On the other hand, in the brane world theory, the dimension of the space-time is larger than four, i.e., there are extra dimensions. Then how to prove the existence of these extra dimensions becomes an important problem. In fact, the development of the extra dimension theory is earlier than the brane world theory, but the latter theory provides a useful method to prove the former, and this method is the localization mechanism mentioned above.By the mechanism of localization, we can obtain the KK modes of matters. What are the KK modes? They are the matter fields in higher dimensional space-time, which are seen in our four-dimensional world. So they must reflect the property of higher di-mensional space-time (extra dimensional space-time) through their masses. By analyzing the mass spectrum of the KK modes, we can know the properties of higher dimensional space-time.In the investigation, we also find some special KK modes (zero modes). They can be localized on the brane with some conditions. And the localized zero modes are in-dependent and free from the extra dimensions. Thus the localized zero modes might be regarded as the matter fields on the brane. And the aim of localizing the known matter field on the brane is realized. So it can be seen the importance of studying the localization of matter fields and their KK modes on the brane. The mass spectrum of the KK modes is determined by the type of brane models.We mainly investigate the matter fields and their KK modes in three interesting types of brane models in this thesis. Firstly, we consider the GRS-inspired brane world. In this model, there are both thin and thick branes at the same time. The zero modes of the scalar and fermion fields can be localized on the brane, and some massive bound or resonant KK modes appear. However, the vector field cannot be localized on the brane. In order to solve this problem, we propose the thick brane model with finite extra dimension (including the single brane model and the split brane one). Because of the finiteness of the extra dimension, the vector can be trapped on the brane. At last, we generalize the brane world in five-dimensional space-time to any dimension, i.e., the p-brane. We get the solutions of some representative types of p-brane, and investigate the localization of q-form fields in this brane. The effect of the spatial dimensions p in the localization of any form field is found, and this result not only covers the cases in five dimensional space-time for the scalar field (q=0) and the vector field (q=1), but also gives some new predictions for the higher dimensional space-time.Although the localization mechanism in this thesis is ideal and preliminary, it also theoretically offers a way to prove the rationality (to localize the known matter on the brane) and the truth (the existence of the extra dimensions) of the brane theory. The existence of extra dimension(s) might be proved in future experiments on the correction to Newton potential from KK gravitons, and the correction to Coulomb potential from KK gauge bosons. And this is our further work.