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 η/s is small, such as the AdS/CFT bound 1/4π, the real part of the dielectric function deviates from the ideal chromohydrodynamic case (η/s=0) slightly. With the increase of η/s, its deviation becomes larger. Meanwhile, the imaginary part exhibits the similar properties. In addition, at some modes of ω/k, 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.