Spacetime Entanglement Entropy: Covariance and Discreteness
| Autor: | Mathur, Abhishek, Surya, Sumati, X, Nomaan |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10714-022-02948-x |
| Popis: | We review some recent results on Sorkin's spacetime formulation of the entanglement entropy (SSEE) for a free quantum scalar field both in the continuum and in manifold-like causal sets. The SSEE for a causal diamond in a 2d cylinder spacetime has been shown to have a Calabrese-Cardy form, while for de Sitter and Schwarzschild de Sitter horizons in dimensions $d>2$, it matches the mode-wise von-Neumann entropy. In these continuum examples the SSEE is regulated by imposing a UV cut-off. Manifold-like causal sets come with a natural covariant spacetime cut-off and thus provide an arena to study regulated QFT. However, the SSEE for different manifold like causal sets in $d=2$ and $d=4$ has been shown to exhibit a volume rather than an area law. The area law is recovered only when an additional UV cut-off is implemented in the scaling regime of the spectrum which mimics the continuum behaviour. We discuss the implications of these results and suggest that a volume-law may be a manifestation of the fundamental non-locality of causal sets and a sign of new UV physics. Comment: 26 pages, 12 figures, to appear in a special issue of Gen. Rel. Grav. in memory of Prof. Thanu Padmanabhan ("Paddy") |
| Databáze: | arXiv |
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