Islands and dynamics at the interface

We investigate a family of models described by two
holographic CFT_2s coupled along a shared interface. The bulk dual
geometry consists of two AdS_3 spacetimes truncated by a shared
Karch-Randall end-of-the-world (EOW) brane. A lower dimensional
effective model comprising of JT gravity coupled to two flat CFT_2
baths is subsequently realized by considering small fluctuations on the
EOW brane and implementing a partial Randall-Sundrum reduction where the
transverse fluctuations of the EOW brane is identified as the dilaton
field. We compute the generalized entanglement entropy for bipartite
states through the island prescription in the effective lower
dimensional picture and obtain precise agreement with the corresponding
doubly holographic computations in the bulk geometry, in the limit of
large brane tension. Furthermore we analyze the replica wormhole saddle
in the gravitational path integral by solving a "conformal
welding problem" and observe that as the replica number n goes to 1, the
presence of these wormholes leads to the island formula.