On analytic descriptions of two-dimensional surfaces associated with the CP^(N-1) sigma model

TL;DR

This paper provides explicit analytic descriptions of 2D surfaces derived from the CP^(N-1) sigma model, demonstrating their equivalence via two different parametrizations, the generalized Weierstrass formula and the Sym-Tafel formula.

Contribution

It introduces explicit formulas for surfaces associated with the CP^(N-1) sigma model and shows their equivalence through two different parametrizations.

Findings

Surfaces are explicitly described using the generalized Weierstrass formula.

These surfaces coincide with those obtained from the Sym-Tafel formula.

Both parametrizations describe the same surface in R^(N^2-1).

Abstract

We study analytic descriptions of conformal immersions of the Riemann sphere S^2 into the CP^(N-1) sigma model. In particular, an explicit expression for two-dimensional (2-D) surfaces, obtained from the generalized Weierstrass formula, is given. It is also demonstrated that these surfaces coincide with the ones obtained from the Sym-Tafel formula. These two approaches correspond to parametrizations of one and the same surface in R^(N^2-1).