Schwinger-Keldysh effective action for relativistic Brownian particle in AdS-CFT

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-AdS 5 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.

Holographic Schwinger-Keldysh field theory of SU(2) diffusion

“…The results of [1,30] are in perfect agreement with that constructed within the non-equilibrium EFT framework [3]. Recently, the holographic SK contour [1] attracted a lot of attention in various holographic settings [2,[38][39][40][41][42][43][44][45][46].…”

Holographic Schwinger-Keldysh field theory of SU(2) diffusion

“…The results of [1,29] are in perfect agreement with that constructed within the non-equilibrium EFT framework [2]. Recently, the holographic SK contour [1] attracted a lot of attention in various holographic settings [37][38][39][40][41][42][43][44][45][46].…”

Nonlinear effective dynamics of a Brownian particle in magnetized plasma

“…When u varies along the radial contour of Figure 3, linearized EOMs (3.36) have been studied in [5,58] when B = 0. The basic idea [58] is as follows.…”

“…When u varies along the radial contour of Figure 3, linearized EOMs (3.36) have been studied in [5,58] when B = 0. The basic idea [58] is as follows. First, one cuts the radial contour of Figure 3 at the rightmost point u = 1 + .…”

“…Obviously, the task of solving linearized EOMs (3.36) reduces to searching for ingoing solutions Φ ig T,L (u, ω). Expressed in the form (3.40), the linearized solutions demonstrate explicit timereversal symmetry [56,58]. Importantly, ingoing modes Φ ig T,L (u, ω) are regular over the entire radial contour and can be constructed for u varying on either upper branch or lower branch.…”