2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/204024It 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.18 pages, 2 figures, v2: reference addedHigh Energy Physics - TheoryHigh Energy Physics - Latticetext