Glassy Transition and Aging in a Model Without Disorder

We study the off-equilibrium relaxational dynamics of the Amit-Roginsky ${\phi }^3$ 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, similar to what is found in long range spin glasses. This is an example of how the mode coupling theory of the structural glass transition can be generalized to off-equilibrium situations.