Universal properties of the Langevin diffusion coefficients

We show that in generic isotropic holographic theories the longitudinal Langevin diffusion coefficient along the string motion is larger compared to that of the transverse direction. We argue that this is in general a universal relation and we derive the generic conditions in order to be satisfied. A way to violate the relation is to consider anisotropic gauge/gravity dualities. We give an explicit example of this violation where the noise along the transverse direction is larger than the noise occurring along the quark motion. Moreover, we derive the effective world-sheet temperature for any generic theory and then the conditions for negative excess noise. We argue that isotropic theories cannot have negative excess noise, and we additionally remark that these conditions are difficult to get satisfied, indicating positivity of the excess noise even in a large class of anisotropic holographic theories, implying a strong universal property.