The dielectric function of the viscous quark–gluon plasma

The viscous chromohydrodynamic equations are derived from a kinetic theory to describe the quark–gluon plasma in the presence of the shear viscosity. The equations are solved in the linear response approximation, and the dielectric function is investigated. When image is small, such as the AdS/CFT bound image, the real part of the dielectric function deviates from the ideal chromohydrodynamic case (image) slightly. With the increase of image, its deviation becomes larger. Meanwhile, the imaginary part exhibits the similar properties. In addition, at some modes of image, the real and the imaginary parts are independent on the shear viscosity. By analyzing the mathematical structures of the dielectric function, we give some explanations for the behavior.