Strange Metals in One Spatial Dimension

TL;DR

This work analyzes a 1+1D SU($N$) gauge theory with adjoint Dirac fermions at finite density, revealing a deconfined gauge-charged Fermi surface in the high-density limit. The low-energy sector maps to a coset CFT with central charge $c=(N^2-1)/3$ and emergent ${\mathcal N}=(2,2)$ supersymmetry, enabling exact scaling dimensions for Friedel oscillations and pairing correlations (both $\Delta=1/3$ for relevant cases). For $N\ge 3$ the fixed point is destabilized by a relevant perturbation, while the large-$N$ limit suggests a rich symmetry structure and potential AdS$_3$ or higher-spin dual descriptions. The low-density regime is probed via DLCQ, uncovering a dense spectrum of bound states whose masses imply a nontrivial interplay between gauge-charged states and density, and hinting that the gauge-charged Fermi-sea picture may extend to low densities. Together, these results provide a controlled, exactly solvable framework for non-Fermi liquid behavior in low-dimensional gauge theories and inform potential holographic dual descriptions.

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.

Figures (4)

• Figure 1: Energy dispersion of the Dirac fermions as a function of momentum. The full line is the zero of energy. The shaded region represents the occupied states. The filled circles are at $\pm k_F$.
• Figure 2: The spectrum of fermionic bound states for $K=5,7,9,11,13,15,17,19$. The states with the same $K$ are shown using the same color. Increasing $K$ for fixed $Q$ is illustrated by a gradual shift to the right in each of the columns.
• Figure 3: The spectrum $M/Q$ of lightest states as a function of $1/K$ for $Q=3,5,7,9,11$. The lines are linear fits to the available data. The points for $Q=3$ have the largest $M/Q$. For each successive $Q$, the $M/Q$ is decreasing. The intercept of the linear fit at $1/K=0$ is the extrapolated value of the $M/Q$ for the lightest state for fixed value of $Q$.
• Figure 4: Spectrum of bosonic bound states for $K=4,6,8,10$. This figure is the analogue of figure \ref{['fullspec']} for the fermionic bound states.