Spacetime entanglement entropy in 1 + 1 dimensions
Sorkin (Expressing entropy globally in terms of (4D) field-correlations arXiv:1205.2953) defines an entropy for a Gaussian scalar field ϕ in an arbitrary region of either a continuous spacetime or a causal set, given only the correlator ⟨ φ ( x ) φ ( y ) ⟩ ?> within the region. The definition is global and independent of any choice of spacelike hypersurface. As a first application, we compute numerically the entanglement entropy in two cases where the asymptotic form is known or suspected from conformal field theory, finding excellent agreement when the required ultraviolet cutoff is implemented as a truncation on spacetime mode sums. We also show how the symmetry of entanglement entropy reflects the fact that RS and SR share the same eigenvalues, with R and S being arbitrary matrices.