The entanglement entropy S(A) = Area(γ_A)/4G. Drag boundary endpoints to explore minimal geodesics in AdS.
Boundary interval length: 120°
RT geodesic length: 0.00
S(A) = L/4G·c/3·ln(...): 0.00
c/3 · log(ℓ/ε): 0.00
Ryu-Takayanagi formula (2006): S(A) = Area(γ_A) / (4G_N), where γ_A is the minimal bulk surface anchored at ∂A.
In AdS₃/CFT₂: geodesic length = 2L·arcsinh(ℓ/(2ε)), giving S(A) = (c/3)·ln(ℓ/ε) matching the CFT result (Calabrese-Cardy).
Drag the orange endpoints on the boundary circle to change region A. The minimal geodesic (purple arc) computes the entropy.
Key insight: Entanglement entropy of a boundary region = area of a bulk minimal surface — geometry encodes quantum information.