Scrambling in Two-Dimensional Conformal Field Theories with Light and Smeared Operators

TL;DR

This paper investigates quantum chaos and scrambling in two-dimensional CFTs at large central charge by analyzing out-of-time-ordered correlators with non-identity Virasoro blocks. It shows that light intermediate channels can delay scrambling, while spatially smearing perturbations on scales smaller than the thermal length can hasten scrambling, yielding a scrambling time that depends on holomorphic/antiholomorphic weights and smear parameters. The results connect the CFT spectrum and perturbation energy to scrambling, with a holographic interpretation in terms of BTZ black hole backreaction and shockwave dynamics. The work clarifies the roles of light primaries and smearing in fast scrambling and outlines avenues for extensions to heavier intermediates, higher dimensions, and refined holographic analyses.

Abstract

We study quantum chaos in two dimensional conformal field theories, building on the work analyzing the out-of-time order thermal correlation functions using large-c Virasoro blocks. Our work investigates the contribution of light intermediate channels and smearing length scales to the four-point function and scrambling. Precise relations for how light intermediate channels increase the scrambling time and how smearing length scales smaller than the thermal length scale decrease the scrambling time are derived.

Figures (2)

• Figure 1: Conformal block $|z^{2h_v} \mathcal{F}_{p}^{II}(z)|$ against time separation $t$ for different values of intermediate channel holomorphic weight $h_{p}$, for $h_{w}=5,h_{v}=1000$ and $c=10^{9}$. Shows the initial exponential growth with $t$ of the conformal block with $h_p > 0$, the decay around scrambling time, and the dominance of light intermediate conformal blocks over the identity block.
• Figure 2: Positions of the point $V$ and $W$ operators prior to integration against Gaussian smearing functions of width $L_V$ and $L_W$.