Glueballs on a transverse lattice

Accurate non-perturbative calculations of glueballs are performed using light-front quantized SU(N) gauge theory, to leading order of the $1/N$ expansion. Based on early work of Bardeen and Pearson, disordered gauge-covariant link variables M on a coarse transverse lattice are used to approximate the physical gauge degrees of freedom. Simple energetics imply that, at lattice spacings of the order of the inverse QCD scale, the effective light-front Hamiltonian can be expanded in gauge-invariant powers of M: a color-dielectric expansion. This leads to a self-consistent constituent structure of bound states. We fix the couplings of this expansion by optimizing Lorentz covariance of low-energy eigenfunctions. To lowest non-trivial order of the expansion, we find a one-parameter trajectory of couplings that enhances Lorentz covariance. On this trajectory the masses of nearly covariant glueball states exhibit approximate scaling, having values consistent with large-N extrapolations of continuum results from other methods. There is very little variation with N in pure Yang-Mills theory: the lightest glueball mass changes by only a few percent between SU(3) and SU(∞). The corresponding light-front wave functions show an unconventional structure. We also examine restoration of rotational invariance in the heavy-source potential.