On Butterfly effect in Higher Derivative Gravities

TL;DR

This paper investigates the butterfly effect in higher derivative gravity theories, revealing the existence of two butterfly velocities influenced by the dimension of operators, with special behavior at critical points.

Contribution

It introduces the concept of dual butterfly velocities in higher derivative gravities and analyzes their behavior in specific models like TMG.

Findings

Higher derivative terms lead to two butterfly velocities.

Velocities depend on the dimension of operators sourced by the metric.

At critical points, the two velocities coincide.

Abstract

We study butterfly effect in $D$-dimensional gravitational theories containing terms quadratic in Ricci scalar and Ricci tensor. One observes that due to higher order derivatives in the corresponding equations of motion there are two butterfly velocities. The velocities are determined by the dimension of operators whose sources are provided by the metric. The three dimensional TMG model is also studied where we get two butterfly velocities at generic point of the moduli space of parameters. At critical point two velocities coincide.