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arXiv:2609.19247

Topological entanglement entropy in 3D gravity

Vijay Balasubramanian, Charlie Cummings

hep-thcond-mat.str-elgr-qcquant-phSubmitted Sep 16, 2026• Announced Sep 18, 2026• 0 citations
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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.

Comments
71+6 pages, 12 figures

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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 GNG_NGN​), 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.
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