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

Overview

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.

Context

Shock-wave solutions and entanglement-wedge reconstruction provide two ways to calculate the butterfly velocity. The preprint asks why their results agree.

Main result

The authors reformulate both computations as inserting initial data into gravitational constraint equations. They interpret the agreement through the similar structure of the initial data and reformulated calculations.

Why it matters

Provides a common canonical description of the two computations examined in this preprint, making the shared role of initial data and gravitational constraints explicit.

Citation

@article{Deng:251204498,
  author = {Deng, Feiyu and Wang, Xiao-Shuai and Wu, Jie-qiang},
  title = {An Interpretation for the Equivalence of Two Holographic Computations of the Butterfly Velocity with the Canonical Formalism of Gravity},
  year = {2025},
  eprint = {2512.04498},
  archivePrefix = {arXiv},
  primaryClass = {hep-th}
}