Invariant formulation of surfaces associated with $CP^{N-1}$ models

TL;DR

This paper develops an invariant mathematical framework for integrable $CP^{N-1}$ sigma models on the Riemann sphere, emphasizing projection operators and exploring associated surfaces and spectral problems.

Contribution

It introduces an invariant formulation using projection operators for $CP^{N-1}$ models, enhancing understanding of their geometric and spectral properties.

Findings

Invariant equations expressed via projection operators.

Detailed analysis of surfaces related to $CP^{N-1}$ models.

Discussion of wave functions in the spectral problem.

Abstract

In this paper, we provide an invariant formulation of completely integrable $CP^{N-1}$ Euclidean sigma models in two dimensions defined on the Riemann sphere $S^2$. The scaling invariance is explicitly taken into account by expressing all the equations in terms of projection operators. Properties of the projectors mapping onto one-dimensional subspaces are discussed in detail. The paper includes a discussion of surfaces connected with the $CP^{N-1}$ models and the wave functions of their linear spectral problem.