Geometric Entropy and Hagedorn/Deconfinement Transition
  It has recently been proposed that the entanglement entropy can be an order parameter of confinement/deconfinement transitions. To find a clear evidence, we introduce a new quantity called the geometric entropy, which is related to the entanglement entropy via a double Wick rotation. We analyze the geometric entropy and manifestly show that its value becomes discontinuous at the Hagedorn temperature both in the free N =4 super Yang-Mills and in its supergravity dual. 
Mitsutoshi Fujita, Tatsuma Nishioka and Tadashi Takayanagi