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

For a conformal field theory (cft) deformed by a relevant operator, the entanglement entropy of a ball-shaped region 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 r d , the entanglement entropy calculation gives rise to terms scaling as r 2δ, where δ is the dimension of the deforming operator. when $$ vardelta le frac{d}{2} $$ , the latter terms dominate the former, and suggest that a modification to the conjecture is needed.