# Real Time Dynamics in Low Point Correlators in 2d BCFT

## TL;DR

This paper explores how low-point correlation functions in 2D boundary conformal field theories encode complex dynamical features like chaos and pole-skipping, revealing insights into higher-point correlations.

## Contribution

It demonstrates that 3-point functions can reveal out-of-time-ordered features and pole-skipping in 2D BCFTs, connecting low-point correlators to chaotic dynamics.

## Key findings

- 3-point functions capture out-of-time-ordered features
- Pole-skipping appears in 2-point functions of 2D BCFTs
- Pole-skipping relates to maximal Lyapunov exponent

## Abstract

In this article, we demonstrate how a 3-point correlation function can capture the out-of-time-ordered features of a higher point correlation function, in the context of a conformal field theory (CFT) with a boundary, in two dimensions. Our general analyses of the analytic structures are independent of the details of the CFT and the operators, however, to demonstrate a Lyapunov growth we focus on the Virasoro identity block in large-c CFT's. Motivated by this, we also show that the phenomenon of pole-skipping is present in a 2-point correlation function in a two-dimensional CFT with a boundary. This pole-skipping is related, by an analytic continuation, to the maximal Lyapunov exponent for maximally chaotic systems. Our results hint that, the dynamical content of higher point correlation functions, in certain cases, may be encrypted within low-point correlation functions, and analytic properties thereof.