Current Algebra Approach to 2d Chiral Metals

We reinterpret Balents and Fisher's free 2d chiral metal [Phys. Rev. Lett. 76, 2782 (1996)] as a chiral U(N) Wess-Zumino-Witten model at level k = 1. Here, the U(N) symmetry relates the N →∞ low-energy excitations about the chiral Fermi surface. We obtain non-Fermi liquid generalizations of the free chiral metal that maintain the U(N) symmetry of the k=1 theory by taking the level to be a positive integer k>1. We calculate two-point correlation functions of the U(1) number density and current operators in these theories for general k. We find k to provide an overall rescaling of the amplitude of these correlation functions. This construction illustrates the ersatz Fermi liquid proposal of Else, Thorgren, and Senthil [Phys. Rev. X 11, 021005 (2021)].