Strange Metals in One Spatial Dimension

TL;DR

This paper analyzes a 1+1 dimensional SU(N) gauge theory with fermions at various densities, revealing a deconfined Fermi surface state with emergent supersymmetry and exact operator scaling dimensions, and explores its dual descriptions.

Contribution

It provides an exact characterization of the high-density phase, including emergent supersymmetry and operator dimensions, and investigates the low-density bound state spectrum.

Findings

High-density phase exhibits a coset conformal field theory with emergent N=(2,2) supersymmetry.

Exact scaling dimensions of operators related to Friedel oscillations and pairing are determined.

For N>2, relevant perturbations are allowed, indicating potential instabilities or phase transitions.

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->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.