Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model

We study the entanglement islands and subsystem volume complexity corresponding to the left/ right entanglement of a conformal defect in d-dimensions in Randall-Sundrum (RS) braneworld model with subcritical tension brane. The left and right modes of the defect mimic the eternal black hole and radiation system respectively. Hence the entanglement entropy between the two follows an eternal black hole Page curve which is unitarity compatible. We compute the volumes corresponding to the left and right branes with preferred Ryu-Takanayagi (RT) surfaces at different times, which provide a probe of the subregion complexity of the black hole and the radiation states respectively. An interesting jump in volume is found at Page time, where the entanglement curve is saturated due to the inclusion of the island surfaces. We explain various possibilities of this phase transition in complexity at Page time and argue how these results match with a covariant proposal qualitatively.

Automated summary

The study focuses on entanglement islands and subsystem volume complexity of a conformal defect in d-dimensions within the Randall-Sundrum (RS) braneworld model. The left and right modes of the defect mimic an eternal black hole and radiation system, leading to a unitarity-compatible Page curve for the entanglement entropy. The volumes corresponding to the left and right branes show an interesting jump at Page time, indicating a complexity phase transition.