  The one-plaquette Hamiltonian of large N lattice gauge theory offers a
constructive model of a $1+1$-dimensional string theory with a stable ground
state.
  The free energy is found to be equivalent to the partition function of a
string where the world sheet is discretized by even polygons with signature and
the link factor is given by a non-Gaussian propagator.
  At large, but finite, N we derive the nonperturbative density of states from
the WKB wave function and the dispersion relations. This is expressible as an
infinite, but convergent, series with the inverse of the hypergeometric
function replacing the harmonic oscillator spectrum of the $1+1$-dimensional
string. In the scaling limit, the series is shown to be finite, containing both
the perturbative (asymptotic) expansion of the inverted harmonic oscillator
model, and a nonperturbative piece that survives the scaling limit.
