  I point out that standard two dimensional, asymptotically free, non-linear
sigma models, supplemented with terms giving a mass to the would-be Goldstone
bosons, share many properties with four dimensional supersymmetric gauge
theories, and are tractable even in the non-supersymmetric cases. The space of
mass parameters gets quantum corrections analogous to what was found on the
moduli space of the supersymmetric gauge theories. I focus on a simple purely
bosonic example exhibiting many interesting phenomena: massless solitons and
bound states, Argyres-Douglas-like CFTs and duality in the infrared, and
rearrangement of the spectrum of stable states from weak to strong coupling. At
the singularities on the space of parameters, the model can be described by a
continuous theory of randomly branched polymers, which is defined beyond
perturbation theory by taking an appropriate double scaling limit.
