Algebras for generalized entanglement wedges

TL;DR

This paper explores the algebraic structure of generalized entanglement wedges in non-AdS spacetimes, proposing a map to algebras and a generalized entropy formula that extend holographic principles beyond traditional settings.

Contribution

It introduces a hypothesis linking generalized entanglement wedges to algebras and proposes a generalized entropy formula, extending holographic entanglement concepts to broader spacetimes.

Findings

Proposes a map from entanglement wedges to algebras.

Suggests a generalized Ryu-Takayanagi formula for entropy.

Shows that algebraic entropy inequalities imply properties of entanglement wedges.

Abstract

In asymptotically AdS spacetimes, the mathematical structure of the set of entanglement wedges reflects the algebraic structure of the underlying holographic description. For more general spacetimes, Bousso and Penington (BP) have recently proposed a generalization of entanglement wedges sharing many of the same properties as usual entanglement wedges. In this paper, we explore the hypothesis that each generalized entanglement wedge can be associated with an algebra in the (generally unknown) fundamental description (in a semiclassical limit). We postulate features of the map from entanglement wedges to algebras that provide a natural algebraic interpretation for some of the basic mathematical properties of the set of entanglement wedges. Quantitatively, we suggest a possible generalization of the Ryu-Takayanagi formula that associates the gravitational entropy of a generalized entanglement wedge with an entropic quantity for the associated algebra. Through this assignment, inclusion monotonicity and strong-subadditivity properties shown by BP for generalized entanglement wedges would follow from various inequalities satisfied by algebraic entropies. We include a detailed appendix reviewing relevant algebraic background, including a discussion of algebraic entropies and their inequalities.