Holographic Reflected Entropy and Islands in Interface CFTs

Abstract: We investigate the reflected entropy for various mixed state configurations in the two dimensional holographic conformal field theories sharing a common interface (ICFTs). In the AdS$3$/ICFT$_2$ framework, we compute the holographic reflected entropy for the required configurations in the vacuum state of the ICFT${\text{2}}$ which is given by twice the entanglement wedge cross section (EWCS) in a spacetime involving two AdS$3$ geometries glued along a thin interface brane. Subsequently, we evaluate the EWCS in the bulk geometry involving eternal BTZ black strings with an AdS$_2$ interface brane, which is dual to an ICFT$_2$ in the thermofield double (TFD) state. We explore the system from a doubly holographic perspective and determine the island contributions to the reflected entropy in the two dimensional semi-classical description involving two CFT${\text{2}}$s coupled to an AdS$_2$ brane. We demonstrate that the results from the island formula match precisely with the bulk AdS$_3$ results in the large tension limit of the interface brane. We illustrate that the phase structure of the reflected entropy is quite rich involving many novel induced island phases and demonstrate that it obeys the expected Page curve for the reflected entropy in a radiation bath coupled to the AdS$_2$ black hole.