### Abstract

We give, for the first time, self-consistent large-N analytical solutions of inhomogeneous condensates in the quantum ℂP^{N − 1} model in the large-N limit. We find a map from a set of gap equations of the ℂP^{N − 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 ℂP^{N − 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 ℂP^{N − 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 ℂP^{N − 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 language | English |
---|---|

Article number | 145 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2017 Dec 1 |

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### Keywords

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

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂP ^{N − 1} model.** / Nitta, Muneto; Yoshii, Ryosuke.

Research output: Contribution to journal › Article

^{N − 1}model',

*Journal of High Energy Physics*, vol. 2017, no. 12, 145. https://doi.org/10.1007/JHEP12(2017)145

}

TY - JOUR

T1 - Self-consistent large-N analytical solutions of inhomogeneous condensates in quantum ℂP N − 1 model

AU - Nitta, Muneto

AU - Yoshii, Ryosuke

PY - 2017/12/1

Y1 - 2017/12/1

N2 - 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.

AB - 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.

KW - 1/N Expansion

KW - Field Theories in Lower Dimensions

KW - Sigma Models

UR - http://www.scopus.com/inward/record.url?scp=85040060129&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040060129&partnerID=8YFLogxK

U2 - 10.1007/JHEP12(2017)145

DO - 10.1007/JHEP12(2017)145

M3 - Article

AN - SCOPUS:85040060129

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

SN - 1126-6708

IS - 12

M1 - 145

ER -