  We discuss in details a simple, purely bosonic, quantum field theory
belonging to larger class of models with the following properties: a) They are
asymptotically free, with a dynamically generated mass scale. b) They have a
space of parameters which gets quantum corrections drastically modifying the
classical singularity structure. The quantum theory can have massless solitons,
Argyres-Douglas-like CFTs, exhibit confinement, etc... c) The physics can, to a
large extent, be worked out in models with a large number of supersymmetries as
well as in purely bosonic ones. In the former case, exact BPS mass formulas can
be derived, brane constructions and embedding in M theory do exist. d) The
models have an interesting 1/N expansion, and it is possible to define a double
scaling limit in the sense of the ``old'' matrix models when approaching the
singularities in parameter space. These properties make these theories very
good toy models for four dimensional gauge theories with Higgs fields, and
provide a framework where the effects of breaking supersymmetry can be
explicitly studied. In our model, we work out in details the quantum space of
parameters. We obtain the non-local lagrangian description of the
Argyres-Douglas-like CFT, and show that it admits a strongly coupled fixed
point. We also explicitly demonstrate property d). The possibility of defining
such double scaling limits was not anticipated on the gauge theory side, and
could be of interest to understand the gauge theory/string theory
correspondence.
