Algebra of diffeomorphism-invariant observables in Jackiw-Teitelboim Gravity

TL;DR

This paper computes the algebra of diffeomorphism-invariant observables in classical Jackiw-Teitelboim gravity, revealing insights into wormholes, matter symmetries, and boundary energy dynamics with a method that extends beyond 2D.

Contribution

It introduces a covariant Peierls bracket approach to analyze observables in JT gravity, avoiding unphysical degrees of freedom and generalizing to higher dimensions.

Findings

Algebra of observables encodes wormhole and matter symmetry results.

Clarifies when bulk excitations affect boundary energy.

Demonstrates robustness of results in higher-dimensional models.

Abstract

In this paper we use the covariant Peierls bracket to compute the algebra of a sizable number of diffeomorphism-invariant observables in classical Jackiw-Teitelboim gravity coupled to fairly arbitrary matter. We then show that many recent results, including the construction of traversable wormholes, the existence of a family of $SL(2,\mathbb{R})$ algebras acting on the matter fields, and the calculation of the scrambling time, can be recast as simple consequences of this algebra. We also use it to clarify the question of when the creation of an excitation deep in the bulk increases or decreases the boundary energy, which is of crucial importance for the "typical state" versions of the firewall paradox. Unlike the "Schwarzian" or "boundary particle" formalism, our techniques involve no unphysical degrees of freedom and naturally generalize to higher dimensions. We do a few higher-dimensional calculations to illustrate this, which indicate that the results we obtain in JT gravity are fairly robust.