Computations Of Transport Coefficients For A Holographic Charged Fluid

In recent years,a novel state of QCD matter,quark-gluon plasma,was created in heavy ion collisions at the RHIC and LHC experiments.It is found that the proper-ties of the quark-gluon plasma could be described by relativistic fluid dynamics,with very small dissipation.The strongly-coupled nature of the quark-gluon plasma renders direct calculations of transport coefficients from perturbative QCD extremely difficult.The AdS/CFT correspondence is a strong-weak duality,and,thus,is widely used to study strongly-coupled quantum field theories at finite temperature and finite densities.In the long wavelength and long time limits,the AdS/CFT correspondence turns into the flu-id/gravity correspondence.Particularly,the fluid/gravity correspondence can be used to probe transport properties of the strongly-coupled quark-gluon plasma.In this thesis,we extended the prescription of the original fluid/gravity correspon-dence:in the linearization approximation,all order derivative terms?of fluid-dynamical variables as well as external sources?will be included in the energy-momentum tensor and U?1?current so to guarantee the causality of a relativistic theory.In an asymptotic AdS₅space,we solved the Einstein-Maxwell equations and constructed the general structure of a relativistic charged fluid dynamics,with a focus on the transport coefficients related to the fluid velocity and charge density.We found that,in order to account for all order derivatives,the energy-momentum tensor and the U?1?current should be parameterised by 10 derivative structures,with each acted by a scalar operator of space-time derivative.In the frequency/momentum space,these scalar operators turn into scalar functions of the frequency and momentum,named as transport coefficient functions.Through numerical solving the Einstein-Maxwell equations,we calculated these transport coefficient func-tions.