How Einstein's Equation Emerges From CFT${}_2$

The {\it finiteness} of the entanglement entropies between disjoint subsystems enables us to show that, the dynamical equation of the entanglement entropy in CFT${}_2$ is precisely three dimensional Einstein’s equation. We establish a profound relation between the cosmological constant and CFT${}_2$ entanglement entropy. Thus entanglement entropies induce internal gravitational geometries in CFT${}_2$. Extracting the dual metric from an entanglement entropy becomes a straightforward procedure. Remarkably, we discover that the renormalization group equation is a geometric identity.