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

TL;DR

This paper presents a new exact soliton solution in the Higgs phase of the ${ m C}P^{N-1}$ model on a ring, demonstrating stability and expanding understanding of phase behavior in finite systems.

Contribution

It introduces a self-consistent, exact confining soliton solution in the Higgs phase of the ${ m C}P^{N-1}$ model in the large-$N$ limit, which was not previously known.

Findings

The soliton is stable with all eigenmodes having real, positive energies.

The solution describes a confining soliton in the Higgs phase on a finite ring.

The model exhibits different phases depending on system size, with a new soliton solution in the Higgs phase.

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.