Effective Mass of Holographic Brownian Particle in Rotating Plasma

The dynamic of string fluctuation under rotating BTZ black hole is studied using the method of \cite{Son:2009vu}. We compare the result with previous computation in \cite{Atmaja:2012jg}, with a different method, for the case of co-rotating string. The result gives definite answer that the end of string identified as an external quark at the boundary behaves as Brownian particle with mass is given an effective mass $M_{eff}$ equal to the zero temperature mass of external quark $M_0$ times Lorentz factor $\gamma$ to the power three. We also extend the computation for general case of rotating black hole where the metric is asymptotically $AdS_3$ and the fluctuation is taken only along the co-rotating motion. It shows that the effective mass of the external quark is in general given by $\gamma^3 M_0$.