Confining solitons in the Higgs phase of $\mathbb{C}{P}^{N-1}$ model: Self-consistent exact solutions in large-$N$ limit

Abstract

The quantum $\mathbb{C}{P}^{N-1}$ model is in the confining (or unbroken) phase with a full mass gap in an infinite space, while it is in the Higgs (broken or deconfinement) phase accompanied with Nambu-Goldstone modes in a finite space such as a ring or finite interval smaller than a certain critical size. We find a new self-consistent exact solution describing a soliton in the Higgs phase of the $\mathbb{C}{P}^{N-1}$ model in the large-$N$ limit on a ring. We call it a confining soliton. We show that all eigenmodes have real and positive energy and thus it is stable.

16 pages, 4 figures. v2: Published version

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• Confinement-Deconfinement Crossover in the Lattice $\mathbb{C}{P}^{N-1}$ Model
• Lattice $\mathbb{C}{P}^{N-1}$ model with ${\mathbb{Z}}_N$ twisted boundary condition: bions, adiabatic continuity and pseudo-entropy
• Ground state modulations in the $\mathbb{C}{P}^{N-1}$ model
• Nambu-Jona Lasinio and Nonlinear Sigma Models in Condensed Matter Systems
• Large-$N$ ${\mathbb{CP}}^{N-1}$ sigma model on a Euclidean torus: uniqueness and stability of the vacuum
• Remarks on the large-$N$ $\mathbb{C}{P}^{N-1}$ model