Diffusion and Chaos from near AdS${}_2$ horizons

Abstract

We calculate the thermal diffusivity $D=\hat{I}º/c_{\ddot{I}}$ 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 $\hat{I}”=2$ then this relationship is always given by $D=v_B^2/(2\ddot{I}€T)$.

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