Stringy algebras, stretched horizons, and quantum-connected wormholes

TL;DR

This paper probes stringy holography beyond the supergravity regime by modeling excited string modes as a free tower with a Hagedorn spectrum. It establishes a distal split property: the split between disjoint regions fails at string-scale separations but can be restored at larger separations, with the critical distance tied to the Hagedorn inverse temperature $\beta_H$. The authors define stretched horizons algebraically via the breakdown of factorization, and show that such regions can realize emergent type III von Neumann algebras through an algebraic ER=EPR framework, indicating quantum-connected geometries. These results connect non-local stringy dynamics to holographic entropy constructs and suggest a robust, perturbatively controllable route to finite-tension holography, with potential implications for entanglement structure and quantum gravity in regimes where string excitations are important.

Abstract

While the supergravity limit of AdS/CFT has been extensively explored, the regime in which stringy dynamics dominate, characterized by the emergence of an infinite tower of higher-spin massive modes, is far less understood. In this work, we leverage techniques from algebraic quantum field theory to investigate the extent to which hallmark features of bulk gravity survive at finite string tension and the emergence of intrinsically stringy phenomena. Working in the $g_s\rightarrow 0$ limit, we model excited string modes as free particles and demonstrate that the resulting Hagedorn spectrum leads to the breakdown of the split property, a strengthening of the locality principle, for regions that are within a string length of each other. We propose that this leads to a precise algebraic definition of stretched horizons and stretched quantum extremal surfaces. When stretched horizons exist, there is an associated nontrivial horizon $\star$-algebra. Furthermore, applying the algebraic ER=EPR proposal leads to the emergence of type III von Neumann factors, which provide an intriguing characterization of how such regions can have a quantum Einstein-Rosen bridge even if they are geometrically disjoint.

Figures (10)

• Figure 1: Left: High-energy modes in quantum field theory cause the entanglement between touching regions to be infinite. Right: In a theory of extended strings, the entanglement can diverge even at a finite distance.
• Figure 2: Left: The Penrose diagram of an AdS-Schwarzschild black hole with the stretched horizon of the right exterior region shaded in red. Right: A timeslice of AdS${}_{3}$, where the purple line is the Rindler horizon and the red region is the stretched horizon for the right region. Any algebra with support in the red regions will not factorized from the white region, even though the regions are geometrically disjoint.
• Figure 3: A sketch of the relevant regions in flat space.
• Figure 4: The blue region corresponds to where $j_{0}(f)$ has non-zero support in flat space.
• Figure 5: A picture of the regions under considering in AdS${}_{2}$. $\delta$ is the geodesic distance between the relevant given points.