An Interpretation for the Equivalence of Two Holographic Computations of the Butterfly Velocity with the Canonical Formalism of Gravity

TL;DR

This paper explains the equivalence of two holographic methods for computing butterfly velocity by reformulating them within the canonical formalism of gravity, revealing their structural similarity.

Contribution

It provides a new interpretation of the equivalence using the canonical formalism, unifying two holographic approaches through similar initial data and constraint equations.

Findings

Both computations can be reformulated with similar structures.

The butterfly velocity is derived from initial data in the constraint equations.

The equivalence is explained by the similar form of the reformulated computations.

Abstract

In this paper, we revisit the equivalence of two holographic computations of the butterfly velocity: the computation with the shock wave solution and the computation with the entanglement wedge reconstruction. We provide an interpretation for the equivalence of the two computations with the canonical formalism of gravity. Specifically, by taking use of the canonical formalism, we reformulate both computations into the ones with a similar form. Here, in both reformulated computations, the butterfly velocity is computed from applying a given set of initial data into the constraint equations. And the sets of initial data of both computations have a similar structure. We then interpret the equivalence of the two computations as from the similar form of the reformulated computations.