Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation

الأصل · EN

For a conformal field theory (CFT) deformed by a relevant operator, the entanglement entropy of a ball-shaped region may be computed as a perturbative expansion in the coupling. A similar perturbative expansion exists for excited states near the vacuum. Using these expansions, this work investigates the behavior of excited state entanglement entropies of small, ball-shaped regions. The motivation for these calculations is Jacobson's recent work on the equivalence of the Einstein equation and the hypothesis of maximal vacuum entropy [arXiv:1505.04753], which relies on a conjecture stating that the behavior of these entropies is sufficiently similar to a CFT. In addition to the expected type of terms which scale with the ball radius as Rᵈ, the entanglement entropy calculation gives rise to terms scaling as R²Δ, where Δ is the dimension of the deforming operator. When Δ≤d/2, the latter terms dominate the former, and suggest that a modification to the conjecture is needed.