On instability of ground states in 2D CP(N-1) and O(N) models at large N

TL;DR

This paper reevaluates the energy of inhomogeneous solutions in 2D CP(N-1) and O(N) models at large N, revealing negative energies that challenge their solitonic interpretation and suggest instability of the ground state.

Contribution

It provides a new analysis of the energy of inhomogeneous solutions, questioning their solitonic nature and exploring implications for the true ground state in these models.

Findings

Inhomogeneous solutions have negative energy, contradicting previous soliton interpretations.

Periodic elliptic solutions have lower energy density than homogeneous ground states.

Results extend to O(N) models and supersymmetric extensions.

Abstract

We consider properties of the inhomogeneous solution found recently for \mbox{$\mathbb{CP}^{\,N-1}$} model. The solution was interpreted as a soliton. We reevaluate its energy in three different ways and find that it is negative contrary to the previous claims. Hence, instead of the solitonic interpretation it calls for reconsideration of the issue of the true ground state. While complete resolution is still absent we show that the energy density of the periodic elliptic solution is lower than the energy density of the homogeneous ground state. We also discuss similar solutions for the ${\mathbb{O}}(N)$ model and for SUSY extensions.