Holographic Entanglement Entropy of Multiple Strips

We study holographic entanglement entropy (HEE) of $m$ strips in various holographic theories. We prove that for $m$ strips with equal lengths and equal separations, there are only 2 bulk minimal surfaces. For backgrounds which contain also "disconnected" surfaces, there are only 4 bulk minimal surfaces. Depending on the length of the strips and separation between them, the HEE exhibits first order "geometric" phase transitions between bulk minimal surfaces with different topologies. We study these different phases and display various phase diagrams. For confining geometries with $m$ strips, we find new classes of "disconnected" bulk minimal surfaces, and the resulting phase diagrams have a rich structure. We also study the "entanglement plateau" transition, where we consider the BTZ black hole in global coordinates with 2 strips. It is found that there are 4 bulk minimal surfaces, and the resulting phase diagram is displayed. We perform a general perturbative analysis of the $m$-strip system: including perturbing the CFT and perturbing the length or separation of the strips.