  We consider 1+1 dimensional SU(N) gauge theory coupled to a multiplet of
massive Dirac fermions transforming in the adjoint representation of the gauge
group. The only global symmetry of this theory is a U(1) associated with the
conserved Dirac fermion number, and we study the theory at variable, non-zero
densities. The high density limit is characterized by a deconfined Fermi
surface state with Fermi wavevector equal to that of free gauge-charged
fermions. Its low energy fluctuations are described by a coset conformal field
theory with central charge c=(N^2-1)/3 and an emergent N=(2,2) supersymmetry:
the U(1) fermion number symmetry becomes an R-symmetry. We determine the exact
scaling dimensions of the operators associated with Friedel oscillations and
pairing correlations. For N>2, we find that the symmetries allow relevant
perturbations to this state. We discuss aspects of the N->infty limit, and its
possible dual description in AdS3 involving string theory or higher-spin gauge
theory. We also discuss the low density limit of the theory by computing the
low lying bound state spectrum of the large N gauge theory numerically at zero
density, using discretized light cone quantization.
