  A new transverse lattice model of $3+1$ Yang-Mills theory is constructed by
introducing Wess-Zumino terms into the 2-D unitary non-linear sigma model
action for link fields on a 2-D lattice. The Wess-Zumino terms permit one to
solve the basic non-linear sigma model dynamics of each link, for discrete
values of the bare QCD coupling constant, by applying the representation theory
of non-Abelian current (Kac-Moody) algebras. This construction eliminates the
need to approximate the non-linear sigma model dynamics of each link with a
linear sigma model theory, as in previous transverse lattice formulations. The
non-perturbative behavior of the non-linear sigma model is preserved by this
construction. While the new model is in principle solvable by a combination of
conformal field theory, discrete light-cone, and lattice gauge theory
techniques, it is more realistically suited for study with a Tamm-Dancoff
truncation of excited states. In this context, it may serve as a useful
framework for the study of non-perturbative phenomena in QCD via analytic
techniques.
