How Einstein's Equation Emerges From CFT2
Abstract
The finiteness of the entanglement entropies between disjoint subsystems enables us to show that, the dynamical equation of the entanglement entropy in CFT2 is precisely three dimensional Einstein's equation. We establish a profound relation between the cosmological constant and CFT2 entanglement entropy. Thus entanglement entropies induce internal gravitational geometries in CFT2. Extracting the dual metric from an entanglement entropy becomes a straightforward procedure. Remarkably, we discover that the renormalization group equation is a geometric identity.
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