Holographic drag force with translational symmetry breaking

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 AdS₅ in which parameter α 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 α results in a reduction of the drag force. Moreover, we study the diffusion constant, which falls with increasing α. It will eventually be shown that at lower values of α or μ (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.