2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196285We consider N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group at large N and at finite temperature on a spatial S^3. We show that, at finite weak 't Hooft coupling, the theory is naturally described as a two dimensional Coulomb gas of complex eigenvalues of the Polyakov-Maldacena loop, valued on the cylinder. In the low temperature confined phase the eigenvalues condense onto a strip encircling the cylinder, while the high temperature deconfined phase is characterised by an ellipsoidal droplet of eigenvalues.1+10 pages. 2 figuresHigh Energy Physics - Theorytext