Schwinger-Keldysh effective action for a relativistic Brownian particle in the correspondence

We compute Schwinger-Keldysh effective action for a relativistic heavy quark (with constant background velocity) in strongly coupled supersymmetric Yang-Mills plasma. The holographic dual description involves a noisy trailing string moving in Schwarzschild- black brane. The noise is caused by Hawking radiation emitted from string world sheet horizon. Besides quadratic terms, the effective action contains cubic interactions, which are entirely induced by the constant background velocity. The nonlinear fluctuation-dissipation relations for three-point functions are discussed based on holographic results.