Enhanced Corrections to the Page Curve near Holographic Entanglement Transitions

I will present enhanced corrections to the entanglement entropy of a subsystem in holographic states. These corrections appear near phase transitions in the entanglement entropy due to competing extremal surfaces, and they are holographic avatars of similar corrections previously found in chaotic energy eigenstates. I will first show explicitly how to find these corrections in chaotic eigenstates by summing over contributions of all bulk saddle point solutions, including those that break the replica symmetry, and by making use of fixed-area states. I will then comment on several intriguing features of this tractable example and discuss a way of understanding these enhanced corrections in other, more general holographic examples.