Confining solitons in the Higgs phase of ℂ P N -1 model: self-consistent exact solutions in large- N limit

The quantum 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 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.