Holographic entanglement entropy in $T\overline{T}$-deformed AdS$_3$

In this work, we study the holographic entanglement entropy in AdS$_3$ gravity with the certain mixed boundary condition, which turns out to correspond to $T\bar{T}$-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in $T\bar{T}$-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both $T\bar{T}$-deformed CFTs and cutoff AdS$_3$. Moreover, our result also shows that the deformed holographic entanglement entropy behaves like the zero temperature CFT one for the large deformation parameter. Based on this result, the two intervals entanglement entropy and phase transition between disconnected and connected phase are also studied.