  We describe a non-perturbative procedure for solving from first principles
the light-front Hamiltonian problem of SU(N) pure gauge theory in D spacetime
dimensions (D>2), based on enforcing Lorentz covariance of observables. A
transverse lattice regulator and colour-dielectric link fields are employed,
together with an associated effective potential. We argue that the light-front
vacuum is necessarily trivial for large enough lattice spacing, and clarify why
this leads to an Eguchi-Kawai dimensional reduction of observables to
1+1-dimensions in the infinite N limit. The procedure is then tested by
explicit calculations for 2+1-dimensional SU(infinity) gauge theory, within a
first approximation to the lattice effective potential. We identify a scaling
trajectory which produces Lorentz covariant behaviour for the lightest
glueballs. The predicted masses, in units of the measured string tension, are
in agreement with recent results from conventional Euclidean lattice
simulations. In addition, we obtain the potential between heavy sources and the
structure of the glueballs from their light-front wavefunctions. Finally, we
briefly discuss the extension of these calculations to 3+1-dimensions.
