Glueballs from 1+1 Dimensional Gauge Theories with Transverse Degrees of Freedom

Abstract

We study $1+1$-dimensional $SU(N)$ gauge theories with adjoint scalar matter representations, based on a dimensional truncation of $2+1$ and $3+1$-dimensional pure QCD, which approximate the dynamics of transversely polarized gluons. The glueballs are investigated non-perturbatively using light-front quantisation, detailed spectra and wavefunctions being obtained for the large-$N$ limit. In general there is some qualitative agreement of the spectra with lattice Monte Carlo data from the higher dimensional QCD. From the light-front wavefunctions we calculate (polarized) structure functions and interpret the gluon and spin content of glueballs. We discuss the phase structure of the reduced theories in relation to matrix models for relativistic non-critical strings.