Langevin diffusion in holographic backgrounds with hyperscaling violation

TL;DR

This paper uses holographic methods to analyze the Langevin diffusion of a relativistic heavy quark in hyperscaling violation backgrounds, deriving correlators and constraints on parameters.

Contribution

It introduces a new holographic framework for studying Langevin diffusion in hyperscaling violation backgrounds with detailed analytic results.

Findings

Derived Langevin correlators in hyperscaling violation backgrounds.

Obtained analytic expressions for spectral densities at different frequencies.

Found new constraints on hyperscaling violation parameter θ with quark velocity v.

Abstract

In this note we consider a relativistic heavy quark which moves in the quark-gluon plasmas. By using the holographic methods, we analyze the Langevin diffusion process of this relativistic heavy quark. This heavy quark is described by a trailing string attached to a flavor brane and moving at constant velocity. The fluctuations of this string are related to the thermal correlators and the correlation functions are precisely the kinds of objects that we compute in the gravity dual picture. We obtain the action of the trailing string in hyperscaling violation backgrounds and we then find the equations of motion. These equations lead us to construct the Langevin correlator which helps us to obtain the Langevin constants. Using the Langevin correlators we derive the densities spectral and simple analytic expressions in the small and large frequency limits. We examine our works for planar and $R$-charged black holes with hyperscaling violation and find new constraints on $\theta$ in the presence of velocity $v$.