Notes on Scrambling in Conformal Field Theory

TL;DR

This paper investigates how out-of-time-order correlators in 2D conformal field theories reveal quantum chaos and fast scrambling, especially beyond the Virasoro identity block, with implications for holography and black hole information.

Contribution

It clarifies the role of primary operator superpositions in quantum scrambling and analyzes the impact of higher-dimension operators on correlators beyond the Virasoro identity block.

Findings

Correlators of superpositions of primary operators can quantify quantum scrambling.

Higher-dimension operators can dominate late-time out-of-time-order correlators.

Results provide insights into black hole information paradox and holographic duality.

Abstract

The onset of quantum chaos in quantum field theory may be studied using out-of-time-order correlators at finite temperature. Recent work argued that a timescale logarithmic in the central charge emerged in the context of two-dimensional conformal field theories, provided the intermediate channel was dominated by the Virasoro identity block. This suggests a wide class of conformal field theories exhibit a version of fast scrambling. In the present work we study this idea in more detail. We begin by clarifying to what extent correlators of wavepackets built out of superpositions of primary operators may be used to quantify quantum scrambling. Subject to certain caveats, these results concur with previous work. We then go on to study the contribution of intermediate states beyond the Virasoro identity block. We find that at late times, time-ordered correlators exhibit a familiar decoupling theorem, suppressing the contribution of higher dimension operators. However this is no longer true of the out-of-time-order correlators relevant for the discussion of quantum chaos. We compute the contributions of these conformal blocks to the relevant correlators, and find they are able to dominate in many interesting limits. Interpreting these results in the context of holographic models of quantum gravity, sheds new light on the black hole information problem by exhibiting a class of correlators where bulk effective field theory does not predict its own demise.