Susy CP^(N-1) model and surfaces in R^(N^2-1)

TL;DR

This paper explores the geometric surfaces generated by solutions of the supersymmetric CP^{N-1} model, revealing their structure, curvature properties, and generalization to higher N, with a focus on their mathematical description.

Contribution

It introduces a method to construct surfaces in R^{N^2-1} from supersymmetric CP^{N-1} solutions, extending known results for the N=2 case to higher N.

Findings

Surfaces are described by projectors built from model solutions.

For N=2, the surface is a sphere with constant curvature.

Surfaces for N>2 can be similarly constructed from the projector.

Abstract

We describe surfaces in R^{N^2-1} generated by the holomorphic solutions of the supersymmetric CP^{N-1} model. We show that these surfaces are described by the fundamental projector constructed out of the solutions of this model and that in the CP^{N-1} case the corresponding surface is a sphere. Although the coordinates of the sphere are superfields the sphere's curvature is constant. We show that for N>2 the corresponding surfaces can also be constructed from the similar projector.