Algebraic perturbation theory: traversable wormholes and generalized entropy beyond subleading order

TL;DR

This paper develops an algebraic framework combining crossed product algebras and perturbation theory to analyze black hole information transfer and traversable wormholes, providing new insights into generalized entropy beyond subleading order.

Contribution

It introduces a novel algebraic approach to quantum gravity using perturbative crossed product algebras, extending the understanding of entropy and information transfer in black hole physics.

Findings

New contributions to generalized entropy beyond subleading order.

Analysis of traversable wormhole algebra of observables in AdS space.

Framework for black hole information transfer via non-local modular structures.

Abstract

The crossed product has recently emerged as an important ingredient in describing algebras of observables for quantum field theory and gravity. We combine this with perturbation theory, and study perturbative crossed product algebras obtained from a unitary deformation of the original system. Motivated by the problem of black hole evaporation, we propose an abstract framework in which black hole information can be transferred to Hawking radiation by passing to a perturbative crossed product exhibiting a degree of non-locality in its modular structure. As both a concrete example and a toy model for evaporation, we analyze the algebra of observables of the traversable wormhole in anti-de-Sitter space. We obtain new contributions to the generalized entropy beyond subleading order relative to the original work by Gao, Jafferis, and Wall. We close with some comments on the potential applicability of the algebraic approach to quantum gravity.