Algebras for generalized entanglement wedges

TL;DR

The paper proposes a map W -> (A_W, ω_W) that assigns generalized BP wedges to algebras with states, aiming to provide an algebraic origin for wedge properties within a semiclassical holographic framework. It introduces an algebraic RT-like formula S_gen(W) = S(ω|A_W) - log Ind(E_{Ω→A_W}) + K_Ω and demonstrates how inclusion monotonicity and strong subadditivity of generalized entropy follow from standard algebraic entropy inequalities, with a detailed appendix on algebraic entropy. The authors explore tangible realizations in random tensor networks and discuss direct constructions of gravitational algebras via modular crossed products, drawing connections to AdS/CFT and Leutheusser–Liu type dualities. They outline several future directions, including potential background independence, algebraic derivations of gravitational dynamics, modular Berry phases, gauge-invariant subregions, and QECC perspectives for generalized entanglement wedge algebras.

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.