Explain the role of entanglement in the AdS/CFT correspondence and how it helps to understand the connection between quantum field theories and gravity.

In the AdS/CFT correspondence, entanglement entropy in the boundary conformal field theory (CFT) is related to the geometry of spacetime in the bulk anti-de Sitter (AdS) space. This relationship is exemplified by the Ryu-Takayanagi formula, which connects the entanglement entropy of a region in the CFT to the area of a minimal surface in the AdS space. This connection helps to understand how spacetime geometry and gravity emerge from quantum entanglement, providing insights into quantum gravity and the holographic principle.