  Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions.
The gluon mass is introduced by coupling the gauge field to an SU(N) principal
chiral nonlinear sigma model. The proof of renormalizability relies on the
asymptotic freedom of the sigma model. However, renormalization forces the
gluon mass to infinity. The continuum theory is in a confined phase rather than
a Higgs phase. The physical excitations of the system are hadron-like bound
states of sigma model particles. We calculate the massive spectrum of
meson-like bound states analytically, using the exact S-matrix of the sigma
model. The baryon-like spectrum can be found in principle by solving a quantum
mechanical N-body problem. We remark on the evidence for the confined phase
found for SU(2) in recent lattice simulations by Gongyo and Zwanziger. Their
simulations show evidence for a Higgs-like phase which seems to disappear with
increasing volume, finding agreement with our analysis in the continuum.
