We study the entanglement entropy of excited states in two-dimensional conformal field theories (CFTs). In particular, we consider excited states obtained by acting on a vacuum with primary operators. We show that the entanglement entropy increases by a finite constant amount under its time evolution. Moreover, in rational conformal field theories, we prove that this increase of the (both Renyi and von Neumann) entanglement entropy always coincides with the log of the quantum dimension of the primary operator.

In this paper, we regard the $$ T\overline{T}/J\overline{T} $$T T ¯ / J T ¯ -deformed CFTs as perturbation theories and calculate the first order correction of the correlation functions due to the $$ T\overline{T}/J\overline{T} $$T T ¯ / J T ¯ ­deformation. As applications, we study the Rényi entanglement entropy of excited state in the $$ T\overline{T}/J\overline{T} $$T T ¯ / J T ¯ -deformed two-dimensional CFTs. We find, up to the first order perturbation of the deformation, the Rényi entanglement entropy of locally excited states will acquire a non­trivial time dependence. The excess of the Rényi entanglement entropy of locally excited state is changed up to order O(c). Furthermore, the out of time ordered correlation function is investigated to confirm that the $$ T\overline{T}/J\overline{T} $$T T ¯ / J T ¯ -deformations do not change the maximal chaotic behavior of holographic CFTs up to the first order of the deformations.