Holographic entanglement entropy for two disjoint intervals in AdS$_3$/CFT$_2$

The Ryu-Takayanagi conjecture contradicts $1+1$-dimensional CFT if we apply it to two far disjoint intervals because it predicts the product state. Instead of the conventional conjecture, we propose a holographic entanglement entropy formula that the entanglement entropy of two disjoint intervals is described by the appropriate sum of the area of signed extremal curves. We confirm that the resulting holographic entanglement entropy is consistent with the entanglement entropy for the specific two disjoint intervals evaluated in the large $c$ limit CFT.