Lorentzian spinfoam gravity path integral and geometrical area-law entanglement entropy
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909883965636608 |
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| author | Han, Muxin |
| author_facet | Han, Muxin |
| contents | This paper investigates entanglement entropy in 3+1 dimensional Lorentzian covariant Loop Quantum Gravity (LQG). We compute the entanglement entropy for a spatial region from states dynamically generated by a spinfoam path integral that sums over a family of 2-complexes. The resulting entropy exhibits a geometric area law, $S \simeq βa$, where the area $a$ of the entangling surface is determined by the LQG area spectrum and the leading coefficient $β>0$ is independent of the underlying 2-complexes. By relating the coupling constant of the sum over 2-complexes to the Barbero-Immirzi parameter $γ$, we reproduce the Bekenstein-Hawking formula for the range $0 < γ\lesssim 1/2$. This work provides a Lorentzian path integral approach to gravitational entropy without the need for contour prescriptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_26925 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lorentzian spinfoam gravity path integral and geometrical area-law entanglement entropy Han, Muxin General Relativity and Quantum Cosmology High Energy Physics - Theory This paper investigates entanglement entropy in 3+1 dimensional Lorentzian covariant Loop Quantum Gravity (LQG). We compute the entanglement entropy for a spatial region from states dynamically generated by a spinfoam path integral that sums over a family of 2-complexes. The resulting entropy exhibits a geometric area law, $S \simeq βa$, where the area $a$ of the entangling surface is determined by the LQG area spectrum and the leading coefficient $β>0$ is independent of the underlying 2-complexes. By relating the coupling constant of the sum over 2-complexes to the Barbero-Immirzi parameter $γ$, we reproduce the Bekenstein-Hawking formula for the range $0 < γ\lesssim 1/2$. This work provides a Lorentzian path integral approach to gravitational entropy without the need for contour prescriptions. |
| title | Lorentzian spinfoam gravity path integral and geometrical area-law entanglement entropy |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.26925 |