Holographic Entanglement — Ryu-Takayanagi Formula

S_A = Area(γ_A)/4G_N — the minimal geodesic in the AdS₃ bulk computes boundary entanglement entropy

30°
150°
0.92
S_A =
S_B =
S_A+B =
RT formula (2006):
S_A = min_γ∼A Area(γ)/4G_N

In AdS₃/CFT₂ (Poincaré disk):
S_A = (c/3)log(l/ε)

Phase transition at |A| = π: connected ↔ disconnected geodesic wins
Strong subadditivity:
S(A)+S(B) ≥ S(A∪B)+S(A∩B)

Automatically satisfied by RT geodesics — elegant proof via bulk geometry
Click phase transition to see |A|=π critical point where two geodesic topologies exchange dominance.