Spacetime entanglement entropy: covariance and discreteness

• Published in: General relativity and gravitation 2022-07, Vol.54 (7), Article 74
• Main Authors: Mathur, Abhishek, Surya, Sumati, Nomaan, X.
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Classical and Quantum Gravitation; Diamonds; Differential Geometry; Entropy; Gravity; Legislation; Manifolds; Mathematical and Computational Physics; Physics; Physics and Astronomy; Quantum Physics; Relativity Theory; Review Article; Scalars; Spacetime; Theoretical
• ISSN: 0001-7701; 1572-9532
• DOI: 10.1007/s10714-022-02948-x

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.