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

Muneto Nitta, Ryosuke Yoshii

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10 Citations (Scopus)


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 non-trivial 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 (confining) 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.

Original languageEnglish
Article number145
JournalJournal of High Energy Physics
Issue number12
Publication statusPublished - 2017 Dec 1


  • 1/N Expansion
  • Field Theories in Lower Dimensions
  • Sigma Models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


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