# Nonlinear Langevin dynamics via holography

## TL;DR

This paper develops a holographic approach to nonlinear Langevin dynamics for a heavy quark in a strongly coupled plasma, deriving the influence phase and confirming fluctuation-dissipation relations beyond weak coupling.

## Contribution

It introduces a holographic method to compute nonlinear corrections to Langevin dynamics using doubled string configurations in AdS/CFT, extending previous linear models.

## Key findings

- Derived the influence phase for a heavy quark in strongly coupled plasma.
- Confirmed the nonlinear fluctuation-dissipation theorem holographically.
- Validated the consistency of the holographic model with unitarity and thermality.

## Abstract

In this work, we consider non-linear corrections to the Langevin effective theory of a heavy quark moving through a strongly coupled CFT plasma. In AdS/CFT, this system can be identified with that of a string stretched between the boundary and the horizon of an asymptotically AdS black-brane solution. We compute the Feynman-Vernon influence phase for the heavy quark by evaluating the Nambu-Goto action on a doubled string configuration. This configuration is the linearised solution of the string motion in the doubled black-brane geometry which has been proposed as the holographic dual of a thermal Schwinger-Keldysh contour of the CFT. Our expression for the influence phase passes non-trivial consistency conditions arising from the underlying unitarity and thermality of the bath. The local effective theory obeys the recently proposed non-linear fluctuation dissipation theorem relating the non-Gaussianity of thermal noise to the thermal jitter in the damping constant. This furnishes a non-trivial check for the validity of these relations derived in the weak coupling regime.