Gauge/Gravity Duality And Holographic Quantum Chromo Dynamics

The present thesis reviews the research field of gauge/gravity duality and holographic QCD in a systematical and comprehensive way. Starting with a brief history of QCD, it gives detailed introductions on the following topics: large N QCD, RHIC phenomenology, basic conceptions on string theory and the holographic principle. Then, by providing the needed materials to under-stand the gauge/gravity duality such as Conformal Field Theory, Anti-de Sitter spacetime and the near horizon limit of extremal branes, it arrives at the main topic—auge/gravity duality, on which the discussions proceed with the aid of analysing the famous example:AdS5/CFT4duality. After this, it talks about the correspondence of phase transitions in the frame of gauge/string duality in order to bring out the topic of thermodynamical ensemble and phase transitions of black branes. Several works on this field are mentioned including ours—the investiga-tions on the thermodynamical properties of grand canonical ensemble consisting both black brane and bubble. At last, as an application of gauge/gravity duali-ty on the description of low energy QCD, it gives an overview on three presently popular holographic QCD models:the D3-D7, D4-D6and Sakai-Sugimoto model. Another work of us on the D0-D4Sakai-Sugimoto model is also covered in this part.In the work of canonical ensemble of bubble and black brane, we discuss the phase structure of the system. We find that, to a large extent, the phase structure depends on the value of chemical potential on the boundary:when the system doesn’t have a global stable, so the final phase of the system will always be the hot flat space; when global stable exists and the final phase of the system depends on the boundary value of b and R. The most complicated case is that both of them are in (Uφ(1), ug), the result is that if R> b, black brane will be the stable phase but if b> R, bubble will be the stable phase.In the work of D0-D4Sakai-Sugimoto model, we add smeared DO charge in the D4branes and let the ratio of the numbers of two branes be finite in the large Nc limit in order to keep the back reaction of DO branes. Now the dual field theory is chiral perturbation theory in a constant glue condensate background, the meson spectrum and the other parameters of the chiral lagrangian will depend on the DO charge density, which we show in our paper by ways of various plots.