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

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.

20 pages, no figures

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Cited by in corpus (6)

• SUSY Chern-Simons ${\mathbb{CP}}^N$ and baby Skyrme models and their BPS structures
• General solutions of the supersymmetric $\mathbb{C}{P}^2$ sigma model and its generalisation to $\mathbb{C}{P}^{N-1}$
• Supersymmetric versions of the Fokas-Gel'fand formula for immersion
• Holomorphic solutions of the susy grassmannian $\sigma$-model and gauge invariance
• Constant curvature holomorphic solutions of the supersymmetric grassmannian sigma model: the case of $G(2,4)$
• Superforms and the $\mathbb{C}{P}^{N-1}$ supersymmetric sigma model