Holographic drag force with translational symmetry breaking

TL;DR

This paper analytically investigates how translational symmetry breaking influences the holographic drag force and diffusion constant, revealing that increased symmetry breaking reduces these quantities and affects their anisotropic behavior.

Contribution

It introduces a holographic model with asymptotic AdS_5 incorporating TSB parameter {eta} and analytically computes the resulting drag force and diffusion constants, highlighting the effects of TSB.

Findings

Decreased {eta} reduces the drag force.

Higher {eta} lowers the diffusion constant.

Transverse diffusion exceeds longitudinal at low {eta} or chemical potential.

Abstract

In order to investigate how the drag force is affected by translational symmetry breaking (TSB), we utilize a holographic model in which the background metric remains translational symmetric while a graviton mass or other fields in the theory break this symmetry. We calculate analytically the drag force, considering an asymptotic $AdS_5$ in which parameter {\alpha} arises from TSB. This parameter can be intuitively understood as a measure of TSB strength and we anticipate that non-zero values of it will affect the drag force. In this asymptotic AdS5 background, we will demonstrate that a decrease in {\alpha} results in a reduction of the drag force. Moreover, we study the diffusion constant, which falls with increasing {\alpha}. It will eventually be shown that at lower values of {\alpha} or {\mu} (chemical potential), the transverse diffusion coefficient is larger than the longitudinal one, and the speed of the heavy quark has minimal impact on the ratio.