Entanglement entropy, conformal invariance and extrinsic geometry

Sergey N. Solodukhin

doi:10.1016/j.physletb.2008.05.071

paper

Entanglement entropy, conformal invariance and extrinsic geometry

arXiv:0802.3117 · doi:10.1016/j.physletb.2008.05.071

Abstract

We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface $Σ$ that separates two subsystems of quantum strongly coupled $N = 4$ SU(N) superconformal gauge theory. We extend this result and calculate entanglement entropy of a generic 4d conformal field theory. As a byproduct, we obtain a closed-form expression for the entanglement entropy in flat space-time when $Σ$ is sphere $S_{2}$ and when $Σ$ is two-dimensional cylinder. The contribution of the type A conformal anomaly to entanglement entropy is always determined by topology of surface $Σ$ while the dependence of the entropy on the extrinsic geometry of $Σ$ is due to the type B conformal anomaly.

12 pages; minor corrections in (4.8), (4.16); final version to appear in PLB

Entanglement entropy, conformal invariance and extrinsic geometry

Abstract

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