Some Studies On The Holography Of Gravity

The holographic hypothesis states that a quantum theory of gravity in d+1 dimensional spacetime may be well described by physical obervables on the d dimensional boundary to the region. In recent years this proposal has been well concerned and widely believed that it might be viewed as a fundamental principle for any quantum theory of gravity. As an implement of holographic principle, AdS/CFT duality which originated form string theory has been well studied and brings some important achievement. Especially, in these two years it has been applied to the study of the strongly correlated systems in QCD and condensed matter physics. People have constructed holographic models with a goal to explore undisclosed phenomena in hydrodynamics, superconductor, non-Fermion fluid, strange metal as well as quantum Hall effects. Moreover, holographic principle has also been applied to other fields such as holographic universe and holographic dark energy etc.Motivated by the development above, in this thesis we concentrate on the construction of the holographic superconductor models in quasi-topological gravity theory and investigate their properties. Specifically, by introducing scalar field and Yang-Mills gauge field in an AdS black hole background, we study the holographic s-wave and p-wave superconductor models respectively. Our main results and conclusions can be summarized as follows. Firstly, in both models for s-wave and p-wave superconductors, the increase of the higher curvature coupling parameters will make the condensations harder. Secondly, the universal relationωg/Tc≌8 which is obtained in the holographic model of Einstein gravity is unstable, and it will shift with the changes of GB coupling parameter as well as the curvature-cubed interaction parameter. Finally,the conductivity componentσyy, andσxx have different behaviors with the frequency co in the p-wave holographic superconductor. The coherence length depends on the coupling parameter as well.