  We study the nonlinear dynamics of a multi-mode random laser using the
methods of statistical physics of disordered systems. A replica-symmetry
breaking phase transition is predicted as a function of the pump intensity. We
thus show that light propagating in a random non-linear medium displays glassy
behavior, i.e. the photon gas has a multitude of metastable states and a non
vanishing complexity, corresponding to mode-locking processes in random lasers.
The present work reveals the existence of new physical phenomena, and
demonstrates how nonlinear optics and random lasers can be a benchmark for the
modern theory of complex systems and glasses.
