Ryu-Takayanagi formula (2006): S(A) = Area(γ_A)/(4G_N) where γ_A is the minimal bulk surface homologous to A.
In AdS₃/CFT₂: S = (c/3) ln(l/ε) where c is central charge, l is interval length, ε is UV cutoff.
The geodesic in AdS₃ (Poincaré disk) is a semicircle in the bulk connecting the endpoints of A.