Inhomogeneous Phase of the Chiral Gross-Neveu Model

There is substantial evidence that the ground state of the 2D chiral Gross-Neveu model, in the presence of a U(1) fermion number chemical potential μ and in the large N limit, is given by a "chiral spiral"phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite N and T=0 for any μ>0. Our analysis is based on nonabelian bosonization, that relates the model to a U(N)1 Wess-Zumino-Witten model deformed by current-current interactions. In this description, the appearance of the inhomogeneous phase is surprisingly simple. We also rederive the phase diagram of the large N chiral Gross-Neveu model via a direct diagrammatic computation, finding agreement with previous results in the literature.