Glassy transition and aging in a model without disorder.

We study the off-equilibrium relaxational dynamics of the Amit-Roginsky φ 3 field theory, for which the mode coupling approximation is exact. We show that complex phenomena such as aging and ergodicity breaking are present at low temperature, similarly to what is found in long range spin glasses. This is a generalization of mode coupling theory of the structural glass transition to off-equilibrium situations. Recently there has been important progress in the understanding of the off-equilibrium dynamics of disordered systems. Although aging phenomena were discovered experimentally in spin glasses in 1983 [1] and subsequently studied by several groups in spin glasses [2] and many other different disordered systems, only quite recently has a dynamical mean field theory (DMFT) for non-equilibrium phenomena , based on microscopic spin glass models, been put forward [3, 4, 5]. Among the most interesting feaatures which emerge from the theory are the violations at low temperature of time translation invariance (TTI) and of the fluctuation-dissipation theorem (FDT), even for very large times, implying breaking of ergodicity. This breaking of ergodicity can not be described simply as a separation of the phase space into different ergodic components within which the system thermalizes as in usual broken-symmetry phases. Rather, the distribution function continues to spread over larger regions of configuration space as time goes on. This spreading 1