Diffusion and Chaos from near AdS$_2$ horizons

Abstract

We calculate the thermal diffusivity $D = κ/c_ρ$ 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 $Δ= 2$ then this relationship is always given by $D = v_B^2/(2 πT)$.

23 pages, Added references, Added minor comments in Appendix B, Version accepted at JHEP