We calculate the thermal diffusivity $D = \kappa/c_{ \rho}$ and butterfly velocity $v_B$ in holographic models that flow to AdS$_2 \times R^{ d}$ fixed points in the infra-red. We show that both these quantities are governed by the same irrelevant deformation of AdS$_2$ and hence establish a simple relationship between them. When this deformation corresponds to a universal dilaton mode of dimension $\Delta = 2$ then this relationship is always given by $D = v_B^2/(2 \pi T)$.
Categories: hep-th