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arXiv · 1602.01380

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

Antony J. Speranza
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Abstract

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 $R^d$, the entanglement entropy calculation gives rise to terms scaling as $R^{2Δ}$, where $Δ$ is the dimension of the deforming operator. When $Δ\leq\frac{d}{2}$, the latter terms dominate the former, and suggest that a modification to the conjecture is needed.

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Antony J. Speranza. 2016-02-03. Entanglement entropy of excited states in conformal perturbation theory and the Einstein equation. https://doi.org/10.1007/jhep04(2016)105

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