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

Abstract

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 $D=v_B^2/(2\pi T)$.

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

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