Entanglement entropy , conformal invariance and extrinsic geometry

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 S2 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. 1 [email protected]