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, nonzero densities. The high density limit is characterized by a deconfined Fermi surface state with Fermi wave vector 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 $\mathcal{N}=(2,2)$ 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 $N\to \infty$ limit, and its possible dual description in ${\mathrm{AdS}}_3$ 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.

• Received 29 June 2012

DOI:https://doi.org/10.1103/PhysRevD.86.066003