Chaos in CFT dual to rotating BTZ

TL;DR

This paper analyzes out-of-time-order correlators in 2D holographic CFTs dual to rotating BTZ black holes, revealing how chaos manifests through periodic modulation and growth patterns linked to black hole rotation and temperature.

Contribution

It extends the computation of OTOCs to rotating BTZ black holes and CFTs on a circle, clarifying the dual CFT origin of observed chaotic behaviors and Lyapunov exponents.

Findings

OTOCs show periodic modulation in rotating BTZ backgrounds.

Maximal channel contribution is necessary for correct bulk OTOC calculation.

Results explain the Lyapunov growth and sawtooth patterns in dual CFTs.

Abstract

We compute out-of-time-order correlators (OTOCs) in two-dimensional holographic conformal field theories (CFTs) with different left- and right-moving temperatures. Depending on whether the CFT lives on a spatial line or circle, the dual bulk geometry is a boosted BTZ black brane or a rotating BTZ black hole. In the case when the spatial direction is non-compact, we generalise a computation of Roberts and Stanford and show that to reproduce the correct bulk answer a maximal channel contribution needs to be selected when using the identity block approximation. We use the correspondence between global conformal blocks and geodesic Witten diagrams to extend our results to CFTs on a spatial circle. In arXiv:1908.03574 it was shown that the OTOC for a rotating BTZ black hole exhibits a periodic modulation about an average exponential decay with Lyapunov exponent $2\pi/\beta$. In the extremal limit where the black hole is maximally rotating, it was shown in arXiv:2009.08518 that the OTOC exhibits an average cubic growth, on which is superposed a sawtooth pattern which has small periods of Lyapunov growth due to the non-zero temperature of left-movers in the dual CFT. Our computations explain these results from a dual CFT perspective.