Stringy Algebras and Quantum-Connected Wormholes Demonstrate Strengthened Locality Within One String Length

The fundamental connection between gravity and quantum mechanics remains a central challenge in theoretical physics, and understanding how spacetime emerges from quantum entanglement is a key step towards resolving it. Aidan Herderschee and Jonah Kudler-Flam, both from the Institute for Advanced Study, investigate this connection by exploring the behaviour of gravity when stringy effects become dominant, moving beyond traditional approximations. Their work reveals that incorporating these stringy dynamics leads to a breakdown of conventional locality, strengthening the idea that regions very close together exhibit interconnected behaviour. This breakdown allows the researchers to define ‘stretched horizons’ mathematically and, crucially, suggests that these horizons are characterised by a specific type of quantum structure, potentially linking them to the existence of wormholes even when those regions appear disconnected, offering new insights into the long-standing ER=EPR correspondence.

Stringy Dynamics Strengthen Locality at Short Distances

Scientists have achieved a detailed understanding of how quantum fields behave when considering an infinite number of interacting particles, revealing subtle algebraic properties that govern their interactions. The work leverages techniques from algebraic field theory to explore the behavior of string theory in regimes where stringy dynamics dominate, specifically examining the emergence of massive particles and their impact on spacetime. Researchers modelled excited string modes as free particles and demonstrated that this approach leads to a breakdown of the “split property,” a principle related to how local operator algebras factorize, within a distance equivalent to the length of a string. This breakdown, the team discovered, signals a strengthening of the locality principle, suggesting that regions closer than a string length exhibit enhanced interconnectedness.

The research proposes a precise algebraic definition of “stretched horizons” and “stretched extremal surfaces,” concepts crucial in understanding black hole physics and the boundaries of spacetime. When stretched horizons exist, the study reveals an associated “horizon-algebra,” a mathematical structure defining the properties of these boundaries. Applying an “ER=EPR” proposal, scientists found the emergence of type III von Neumann factors, which characterize how seemingly disjoint regions can be connected via Einstein-Rosen bridges, or wormholes. The team rigorously defined a notion of generalized entropy at finite string tension, moving beyond approximations that rely on infinitesimal values.

They demonstrated that the Reeh-Schlieder theorem, a cornerstone of quantum field theory stating that the vacuum state is cyclic and separating for local algebras, continues to hold even when considering an infinite number of interacting fields. Specifically, the team showed that for algebras representing local spacetime regions, the vacuum vector can be approximated to arbitrary precision by a sequence of states, confirming the consistency of the theory. The research establishes that the Hilbert space, representing the possible states of the system, takes the form of a separable Fock space, ensuring its physical meaningfulness. These findings provide a robust framework for exploring the quantum nature of gravity and the fundamental structure of spacetime.

Finite String Tension Breaks Entanglement Split Property

This research investigates the behaviour of gravity and quantum entanglement when considering the fundamental building blocks of string theory, specifically in scenarios where string tension is finite. The team demonstrates that incorporating the finite size of strings leads to a breakdown of the ‘split property’, a principle governing how entanglement behaves between regions of spacetime. This breakdown strengthens the idea that regions separated by distances comparable to the string length exhibit stronger connections than predicted by standard quantum field theory. The work proposes a precise algebraic definition of ‘stretched horizons’ and ‘stretched extremal surfaces’, concepts related to the boundaries of black holes, and reveals that these horizons are associated with a non-trivial algebraic structure.

Furthermore, applying the algebraic ER=EPR proposal, a conjecture linking entanglement with wormholes, leads to the emergence of specific types of mathematical structures called type III von Neumann factors, suggesting a way to characterise connections between seemingly disjoint regions of spacetime. The researchers acknowledge that their analysis primarily focuses on the limit of zero string coupling, where interactions between strings are neglected, and that exploring finite string coupling represents a future direction for research. They also note that these findings are particularly relevant to understanding the BFSS model, a theoretical framework aiming to describe type IIA string theory at finite coupling, and may have implications for experiments probing this regime. Future work will focus on incorporating perturbative corrections to move beyond the zero string coupling limit and further refine the understanding of stringy horizons and their connection to quantum gravity.