Invariant recurrence relations for CP^(N-1) models

Abstract

In this paper, we present invariant recurrence relations for the completely integrable CP^(N-1) Euclidean sigma model in two dimensions defined on the Riemann sphere S^2 when its action functional is finite. We determine the links between successive projection operators, wave functions of the linear spectral problem, and immersion functions of surfaces in the su(N) algebra together with outlines of the proofs. Our formulation preserves the conformal and scaling invariance of these quantities. Certain geometrical aspects of these relations are described. We also discuss the singularities of meromorphic solutions of the CP^(N-1) model and show that they do not affect the invariant quantities. We illustrate the construction procedure through the examples of the CP^2 and CP^3 models.

25 pages

References in corpus (2)

• On analytic descriptions of two-dimensional surfaces associated with the CP^(N-1) sigma model
• Surfaces in ${\mathbb{R}}^{N^2-1}$ based on harmonic maps $S^2\to C{P}^{N-1}$

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• On the surfaces associated with $\mathbb{C}{P}^{N-1}$ models
• On a stack of surfaces obtained from the $\mathbb{C}{P}^{N-1}$ sigma models
• Soliton surfaces associated with CP^{N-1} sigma models
• A cohomological approach to immersed submanifolds via integrable systems
• Minimal surfaces in the soliton surface approach
• $\mathbb{C}{P}^N$ sigma models via the $SU(2)$ coherent states approach
• Superforms and the $\mathbb{C}{P}^{N-1}$ supersymmetric sigma model
• Structural equations of supermanifolds immersed in the superspace ${\mathcal{M}}^{(3|2)}(c)$ with a prescribed curvature
• Properties of soliton surfaces associated with integrable $\mathbb{C}{P}^{N-1}$ sigma models