Strange metals in one spatial dimension

Abstract

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 → ∞ 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.