  We consider a two-dimensional scalar field theory with a nilpotent current
algebra, which is dual to the Principal Chiral Model. The quantum theory is
renormalizable and not asymptotically free: the theory is strongly coupled at
short distances (encountering a Landau pole). We suggest it can serve as a toy
model for $\lambda\phi^{4}$ theory in four dimensions, just as the principal
chiral model is a useful toy model for Yang-Mills theory. We find some
classical wave solutions that survive the strong coupling limit and quantize
them by the collective variable method. They describe excitations with an
unusual dispersion relation $\omega\propto|k|^{\frac{2}{3}}$ . Perhaps they are
the "preons" at strong coupling, whose bound states form massless particles
over long distances.
