Application Of Gauge-Gravity Duality On Polarized Deep Inelastic Scattering

In the thesis, we have focused on the gauge-gravity duality, which gives de-scriptions of QCD-like theory in strong coupling area. With such kind of strong coupling, the perturbation method has always failed to work; instead, new insights and methods are required then. As a successful attempt, the gauge-gravity duality has played an interesting role.The gauge-gravity theory itself is an interesting theory, which can be seen as an example of holographic principle. Indeed, it has covered a lot of interesting theories, including supergravity and gauge theory. Also in such theory, the supersymmetry and extra dimensional methods are essential. That is, the study of theory itself, besides the study of its application, is more important and intriguing. With above motivations, we have finished the paper, which includes:1) The ADM splitting and KK splitting have been studied and compared in the paper. As famous applications, the ADM splitting has given the constrained Hamil-tonian of Einstein's theory; with KK splitting, the attempt has been done to write the four-dimensional gravity and Maxwell's theory into a five-dimensional general relativity. In the paper, we have tried to figure out the relationship between ADM splitting and KK splitting. That is, we have adopted an approach to write down the Ricci scalar from a metric, and with different metrics, different splitting results will be got. While in the process, we have employed two tensors, the physical meaning of which have also been given in the paper. Another attempt we have done is to get the duality relationship between the two splitting, and in the form of matrix, the result can be clearly seen.2) As an application of the gauge-gravity duality, the polarized structure func-tions of neutral hadrons have been calculated, the functions which are generally obtained from the DIS process. The sum rules, direct results of the structure func-tions have also been reviewed. It is interesting to notice that the BC sum rule has failed as predicted by the gauge-gravity duality. Actually, any effective theory with Pauli term will give the same conclusion.As the introduction of background knowledge, we have taken a different road, i.e., in the view of field theory. As often as it is, the general introduction of gauge-gravity duality is done from the supergravity description. While some clues of such duality can be also found in the gauge theory side. Namely, in the limit of large N and large't Hooft parameter, the gauge theory is similar to a string description. While a string theory in four dimensional always needs a new dimension to be a self-consistent theory. From this view, the connections between the five-dimensional gravity and four-dimensional gauge theory is implied. As an important example, the gravity in AdS5×S5 space and four dimensional CFT theory have been linked with each other, which can be seen from the symmetric groups. As a result of such duality, the five-dimensional field can be divided into the boundary value and an operator in the dual four-dimensional theory.