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This research establishes a theoretical bridge between 3D gravity tensor networks and the quantum extremal surface formula, offering a canonical quantization approach that extends beyond time-symmetric spacetimes. By deriving an entropy formula for matter-inclusive states without relying on path integrals, the work advances fundamental understanding of holographic duality in gravitational systems.

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Topological entanglement entropy in 3D gravity

arXivSeptember 18, 20261 min read

arXiv:2609.19247v1 Announce Type: cross Abstract: We derive an entropy formula for a recently proposed tensor network model of states in 3D gravity which satisfy the constraint equations of diffeomorphism invariance, and including the effects of matter. After accounting for the invertibility of the spacetime metric, we argue that this formula matches the quantum extremal surface formula (for small but finite $G_N$), and is not restricted to time symmetric spacetimes. We derive the result via canonical quantization without relying on path integrals, and discuss an extension to compact bulk subregions.

Abstract:We derive an entropy formula for a recently proposed tensor network model of states in 3D gravity which satisfy the constraint equations of diffeomorphism invariance, and including the effects of matter. After accounting for the invertibility of the spacetime metric, we argue that this formula matches the quantum extremal surface formula (for small but finite $G_N$), and is not restricted to time symmetric spacetimes. We derive the result via canonical quantization without relying on path integrals, and discuss an extension to compact bulk subregions.

High Energy Physics - Theory (hep-th); Strongly Correlated Electrons (cond-mat.str-el); General Relativity and Quantum Cosmology (gr-qc); Quantum Physics (quant-ph)

arXiv:2609.19247 [hep-th]

(or arXiv:2609.19247v1 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2609.19247 arXiv-issued DOI via DataCite (pending registration)

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