Constant curvature surfaces of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model

TL;DR

This paper constructs constant curvature surfaces from solutions of the supersymmetric ^{N-1} sigma model, identifying a unique holomorphic solution and extending the analysis to Grassmannian models.

Contribution

It introduces a criterion for constructing non-holomorphic solutions and extends the analysis to supersymmetric Grassmannian models, highlighting the uniqueness of the generalized Veronese curve.

Findings

Unique holomorphic solution leads to constant curvature surfaces

General criterion for non-holomorphic solutions

Extension to supersymmetric Grassmannian models

Abstract

Constant curvature surfaces are constructed from the finite action solutions of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model. It is shown that there is a unique holomorphic solution which leads to constant curvature surfaces: the generalized Veronese curve. We give a general criterion to construct non-holomorphic solutions of the model. We extend our analysis to general supersymmetric Grassmannian models.