In gauge/gravity duality, matrix degrees of freedom on the gauge theory side play important roles for the emergent geometry. In this talk, we discuss how the entanglement on the gravity side can be described as the entanglement between matrix degrees of freedom. Our approach, which we call "matrix entanglement", is different from "target-space entanglement" proposed and discussed recently by several groups. The examples studied include a small black hole in AdS5*S5 that can evaporate without being attached to a heat bath, for which our approach suggests a gauge theory counterpart of the entanglement island behind the horizon. Specifically, we propose that the confined degrees of freedom in the partially-deconfined states correspond to the island. Intuitively, the confined sector consists of D-branes sitting behind the horizon and sourcing the exterior geometry.

This talk is based on work in progress with Vaibhav Gautam, Antal Jevicki and Cheng Peng.