Entanglement Entropy of Compactified Branes and Phase Transition

Understand

We first calculate the holographic entanglement entropy of M5 branes on a circle and see that it has phase transition during decreasing the compactified radius.

• In particular, it is shown that the entanglement entropy scales as $N^3$.
• Next, we investigate the holographic entanglement entropy of D0+D4 system on a circle and see that it scales as $N^2$ at low energy, likes as a gauge theory with instantons.
• However, at high energy it transforms to a phase which scales as $N^3$, like as M5 branes system.