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arXiv · 1204.4160

On Shape Dependence and RG Flow of Entanglement Entropy

Igor R. Klebanov·Tatsuma Nishioka·Silviu S. Pufu·Benjamin R. Safdi
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Abstract

We use a mix of field theoretic and holographic techniques to elucidate various properties of quantum entanglement entropy. In (3+1)-dimensional conformal field theory we study the divergent terms in the entropy when the entangling surface has a conical or a wedge singularity. In (2+1)-dimensional field theory with a mass gap we calculate, for an arbitrary smooth entanglement contour, the expansion of the entropy in inverse odd powers of the mass. We show that the shape-dependent coefficients that arise are even powers of the extrinsic curvature and its derivatives. A useful dual construction of a (2+1)-dimensional theory, which allows us to exhibit these properties, is provided by the CGLP background. This smooth warped throat solution of 11-dimensional supergravity describes renormalization group flow from a conformal field theory in the UV to a gapped one in the IR. For this flow we calculate the recently introduced renormalized entanglement entropy and confirm that it is a monotonic function.

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Igor R. Klebanov, Tatsuma Nishioka, Silviu S. Pufu, Benjamin R. Safdi. 2012-07-12. On Shape Dependence and RG Flow of Entanglement Entropy. https://doi.org/10.1007/jhep07(2012)001

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