Anisotropic Black Brane And Its Applications In Gravity/Gauge Duality

The gauge/gravity duality is a powerful mathematical tool for studying the strongly coupled system. One can translate a strongly coupled gauge field problem on the boundary into a gravitational issue in the bulk by using gauge/gravity duality. This thesis study the quark-gluon plasma and DC conductivities in the frame work of gauge/gravity duality.After giving an overview of the basic concept of gauge/gravity duality, in chapter3, we start with type IIB supergravity and construct a anisotropic holographic duality. We present a anisotropic charged black hole solution dual to N = 4 super Yang-Mills plasma at finite U(1) chemical potential and finite temperature on the boundary of Ad S space.We discuss the thermodynamics of anisotropic gauge field theory via holographic renormalization. Finally, we study the instabilities of thermodynamics and phase structure.We find that, compared with RN-Ad S black hole and the chargeless anisotropic black hole, the presence of anisotropy and U(1) gauge field will enrich the thermal structure of the holographic system.In chapter 4, in the framework of anisotropic duality, we calculate the drag force acting on a massive quark moving through an anisotropic N = 4 S U(N) Super YangMills plasma at U(1) chemical potential. We find that the chemical potential will change the ordering of drag force in di?erent directions.In chapter 5, we use Ad S/CMT correspondence to calculate the holographic DC conductivity, thermal conductivity and thermoelectric conductivity of the dual conformal filed on the boundary in the Gauss-Bonnet-Maxwell theory with momentum dissipation by introducing several anisotropic scalar fields. We can see that DC heat conductivity is independent of the Gauss-Bonnet coupling constant.