Universality, intertwiners and black hole information

TL;DR

The paper develops an algebraic framework for black hole information flow using superselection sectors and intertwiners, arguing that nonlocal correlations in the full quantum gravity algebra extend across the black hole atmosphere and interior. It shows that enlarging the boundary algebra to include intertwiners enables perfect distinguishability of microstates and reproduces the Page curve, while preserving a smooth horizon for infalling observers. By connecting boundary reconstructions, quantum extremal surfaces, and holographic mutual information, the work links entanglement wedge physics to a topologically protected information storage mechanism and to replica-wormhole topologies. The findings suggest a nonperturbative, topology-linked route to unitarity in black hole evaporation, with potential implications for wormholes, islands, and near-horizon quantum gravity effects.

Abstract

The central question in this article is how information does leak out from black holes. Relying on algebraic arguments and the concept of superselection sectors, we propose the existence of certain operators whose correlations extend across the black hole atmosphere and range into the interior. Contained in the full algebra, these black hole intertwiners will not belong to the subalgebra describing semiclassical bulk physics. We study this proposal in the context of operator reconstructions for code spaces containing a large number of microstates. As long as the atmosphere is excluded from a particular subsystem, the global state seen under the action of the associated algebra is maximally mixed and therefore described by a single classical background. Once the relevant correlations are encoded, i.e. if the algebra is sufficiently enlarged, perfect state distinguishability becomes possible. We arrive at this by computing the von Neumann entropy which may explain the result obtained by applying the quantum extremal surface prescription to the mixed state. We then examine these insights in the context of black hole evaporation and argue that information is transferred to the radiation via black hole intertwiners. We derive the Page curve. The mechanism above suggests that black hole information is topologically protected. An infalling observer would experience no drama. This may resolve the unitarity problem without running into any firewall or state puzzle, the latter being evident in generalized entropy computations. We also examine the question of how certain wormhole topologies may be understood given these findings. We argue that their occurrence in gravity replica computations may be related to the maximal correlation between radiation and atmosphere surrounding the old black hole. This may suggest a connection between topology change and near horizon quantum gravitational effects.

Figures (17)

• Figure 1: Thermal black hole in global AdS (left). The dual ensemble lives on the boundary. A typical microstate is dual to an excited heavy state in the CFT (right). In this case, there is no homology constraint on the RT surface associated with a finite boundary subregion. Its entanglement wedge may cover the entire black hole. To distinguish the two setups, we use a dashed circle indicating the black hole when the boundary state is pure.
• Figure 2: Superposition of black hole microstates. For simplicity, we use the notation $\tilde{\Sigma} \equiv \Sigma_i c_i$. The circle in the center (right) is used to represent the pure state.
• Figure 3: Thermal black hole located at the center. The quantum RT surface for the boundary subregion $A$ may change between two different QESs attached to the boundaries of $A$. The first one is homologous to $A$ with area $\mathcal{A}_2$ (cyan). The second one is homologous to the complement $B$ and has area $\mathcal{A}_1$ (purple).
• Figure 4: Holographic bulk intertwiners (green, solid lines) are supported on the bulk region which is enclosed by minimal codimension two surfaces.
• Figure 5: The boundary subregions are complementary to each other. Their entanglement entropy is given by the area of the RT surface (black, solid line). The latter measures the intertwiner correlations (green, dotted lines) ranging across the two subsystems.