General Relativity and Quantum Cosmology
[Submitted on 3 Jul 2022 (v1), last revised 5 Jul 2022 (this version, v2)]
Title:Spacetime Entanglement Entropy: Covariance and Discreteness
View PDFAbstract: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.
Submission history
From: Nomaan X [view email][v1] Sun, 3 Jul 2022 17:18:03 UTC (9,360 KB)
[v2] Tue, 5 Jul 2022 08:21:11 UTC (9,360 KB)
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