Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-02-21
Phys.Lett.B665:305-309,2008
Physics
High Energy Physics
High Energy Physics - Theory
12 pages; minor corrections in (4.8), (4.16); final version to appear in PLB
Scientific paper
10.1016/j.physletb.2008.05.071
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 $\Sigma$ that separates two subsystems of quantum strongly coupled ${\mathcal{N}}=4$ 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 $\Sigma$ is sphere $S_2$ and when $\Sigma$ is two-dimensional cylinder. The contribution of the type A conformal anomaly to entanglement entropy is always determined by topology of surface $\Sigma$ while the dependence of the entropy on the extrinsic geometry of $\Sigma$ is due to the type B conformal anomaly.
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