On the Entanglement Entropy of Quantum Fields in Causal Sets

Abstract

In order to understand the detailed mechanism by which a fundamental discreteness can provide a finite entanglement entropy, we consider the entanglement entropy of two classes of free massless scalar fields on causal sets that are well approximated by causal diamonds in Minkowski spacetime of dimensions 2,3 and 4. The first class is defined from discretised versions of the continuum retarded Green functions, while the second uses the causal set's retarded nonlocal d'Alembertians parametrised by a length scale $l_k$. In both cases we provide numerical evidence that the area law is recovered when the double-cutoff prescription proposed in arXiv:hep-th/1611.10281 is imposed. We discuss in detail the need for this double cutoff by studying the effect of two cutoffs on the quantum field and, in particular, on the entanglement entropy, in isolation. In so doing, we get a novel interpretation for why these two cutoff are necessary, and the different roles they play in making the entanglement entropy on causal sets finite.

arXiv comment36 pages, 14 figures

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Cited by in corpus (8)

• Entanglement Entropy of Causal Set de Sitter Horizons
• Insights on Entanglement Entropy in $1+1$ Dimensional Causal Sets
• Entanglement Entropy of Disjoint Spacetime Intervals in Causal Set Theory
• Lorentzian Spectral Geometry with Causal Sets
• Spacetime Entanglement Entropy of de Sitter and Black Hole Horizons
• Spacetime Entanglement Entropy: Covariance and Discreteness
• Aspects of Quantum Fields on Causal Sets
• Entanglement Entropy and Causal Set Theory