Abstract
We compute Schwinger-Keldysh effective action for a relativistic heavy quark (with constant background velocity) in strongly coupled N = 4 supersymmetric Yang-Mills plasma. The holographic dual description involves a noisy trailing string moving in Schwarzschild-AdS5 black brane. The noise is caused by Hawking radiation emitted from string worldsheet horizon. Besides quadractic 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.
Highlights
Brownian motion of a heavy particle in a thermal bath has become a textbook example [1,2] for understanding fundamental aspects of nonequilibrium statistical mechanics
This study was further extended in a number of aspects: the heavy quark could be relativistic [41,42], the environment would be in a nonequilibrium state corresponding to the time-dependent anti–de Sitter (AdS) black hole [43], the dissipation would be nonlinear [44], etc
II, we present the relativistic trailing string in AdS5 black brane, which is the holographic dual of a relativistic heavy quark in N 1⁄4 4 SYM plasma
Summary
Brownian motion of a heavy particle in a thermal bath has become a textbook example [1,2] for understanding fundamental aspects of nonequilibrium statistical mechanics. This study was further extended in a number of aspects: the heavy quark could be relativistic [41,42], the environment would be in a nonequilibrium state corresponding to the time-dependent AdS black hole [43], the dissipation (the noise) would be nonlinear (non-Gaussian) [44], etc The latter adopted the holographic SK contour [45] (see [46,47,48] for an alternative holographic prescription for the SK contour) and derived the effective action for a nonlinear Langevin theory [10,11]. The cubic interactions generate nonlinear corrections to the relativistic Langevin theory of [41,42], which do not satisfy Kubo-Martin-Schwinger (KMS) conditions for three-point functions of medium force [17,57] This supports the claim that the fluctuations and dissipations caused by the world sheet horizon shall be of nonthermal nature [41].
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