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

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.