Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum CPN-1 model

We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum CPN-1 model in the large-N limit. We find a map from a set of gap equations of the CPN-1 model to those of the Gross-Neveu (GN) model (or the gap equation and the Bogoliubov-de Gennes equation), which enables us to find the self-consistent solutions. We find that the Higgs field of the CPN-1 model is given as a zero mode of solutions of the GN model, and consequently only topologically nontrivial solutions of the GN model yield nontrivial solutions of the CPN-1 model. A stable single soliton is constructed from an anti-kink of the GN model and has a broken (Higgs) phase inside its core, in which CPN-1 modes are localized, with a symmetric (con fi ning) phase outside. We further find a stable periodic soliton lattice constructed from a real kink crystal in the GN model, while the Ablowitz-Kaup-Newell-Segur hierarchy yields multiple solitons at arbitrary separations.