2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/200242We 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 ${\mathcal{N}}=4$ 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 $Σ$ 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 PLBHigh Energy Physics - TheoryStatistical MechanicsGeneral Relativity and Quantum CosmologyDifferential GeometryQuantum Physicstext