Diffusion and chaos from near AdS2 horizons

Abstract

We calculate the thermal diffusivity D = κ/c[subscript ρ] and butterfly velocity v[subscript B] in holographic models that flow to AdS[subscript 2] × R[superscript d] fixed points in the infra-red. We show that both these quantities are governed by the same irrelevant deformation of AdS[subscript 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[subscript B][superscript 2]/(2πT).