Holographic screening length in a hot plasma of two sphere

Abstract

We study the screening length of a quark-antiquark pair moving in a hot plasma living in two sphere $S^2$ manifold using AdS/CFT correspondence where the background metric is four dimensional Schwarzschild-AdS black hole. The geodesic solution of the string ends at the boundary is given by a stationary motion in the equatorial plane as such the separation length $L$ of quark-antiquark pair is parallel to the angular velocity $\omega$. The screening length and the bound energy are computed numerically using Mathematica. We find that the plots are bounded from below by some functions related to the momentum transfer $P_c$ of the drag force configuration. We compare the result by computing the screening length in the quark-antiquark reference frame where the gravity dual are "Boost-AdS" and Kerr-AdS black holes. Finding relations of the parameters of both black holes, we argue that the relation between mass parameters $M_{Sch}$ of the Schwarzschild-AdS black hole and $M_{Kerr}$ of the Kerr-AdS black hole in high temperature is given by $M_{Kerr}=M_{Sch}(1-a^2l^2)^{3/2}$, where $a$ is the angular momentum parameter.