Diffusion and Chaos from near AdS$_2$ horizons

TL;DR

This paper investigates the relationship between thermal diffusivity and butterfly velocity in holographic models with near-AdS2 horizons, revealing a universal connection governed by irrelevant deformations.

Contribution

It establishes a simple, universal relationship between diffusivity and butterfly velocity in models flowing to AdS2 fixed points, linked by irrelevant deformations.

Findings

D = v_B^2/(2 \pi T) when deformation is a universal dilaton mode of dimension 2

Both quantities are governed by the same irrelevant deformation of AdS2

The relationship holds universally for the specified class of models

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