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 \(N \rightarrow \infty\) 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)].