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

Abstract

Abstract The quantum ℂP 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 ℂP 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.