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 mu 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 mu > 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.