On Instability of Ground States in 2D \(\mathbb {CP}^{\,N-1}\) and \(\mathbb {O}^{N}\) Models at Large \(N\)

We consider properties of the inhomogeneous solution found recently for the \(\mathbb {CP}^{\,N-1}\) 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. Abstract Published by the Jagiellonian University 2025 authors