Current algebra approach to two-dimensional interacting chiral metals

Abstract

We reinterpret the chiral $U(N)$ Wess-Zumino-Witten (WZW) model at level $k>1$ in $(1+1)$ dimensions as an interacting chiral metal in two space dimensions. In this reinterpretation, spatial translations along one of the spatial dimensions in the two-dimensional chiral metal arise from a generator of the $U(N)$ symmetry of the WZW model. The WZW model at $k=1$ is equivalent to Balents and Fisher's free chiral metal [L. Balents and M. P. A. Fisher, Phys. Rev. Lett. 76, 2782 (1996)]. Here, the $U(N)$ symmetry corresponds to the IR symmetry of a chiral Fermi gas with (half of a) Fermi surface, with $N$ equal to the number of points on the Fermi surface. We argue that exactly solvable interacting generalizations occur for levels $k>1$. Importantly, these interacting chiral metals maintain the $U(N)$ symmetry of the free system. We calculate two-point correlation functions of the single-particle fermion operator, the $U(1)$ number density, and current operators in these theories for general $k$. We find that interactions ($k>1$) produce $1/N$ corrections to scaling of the single-particle fermion operator as $N\ensuremath{\rightarrow}\ensuremath{\infty}$ and renormalize the amplitudes of the density and current two-point functions. This construction illustrates the ersatz Fermi liquid proposal of Else et al. [Phys. Rev. X 11, 021005 (2021)].