General solutions of the supersymmetric $\mathbb{C}P^2$ sigma model and its generalisation to $\mathbb{C}P^{N-1}$

TL;DR

This paper introduces a novel method for constructing finite action solutions in the supersymmetric B2 sigma model, revealing more non-holomorphic solutions and generalizing to higher dimensions.

Contribution

The paper presents a new approach that yields more non-holomorphic solutions for the supersymmetric B2 sigma model and extends it to B3 and beyond.

Findings

More non-holomorphic solutions identified

Explicit solutions for B2 model provided

Method generalized to B4 and higher

Abstract

A new approach for the construction of finite action solutions of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model is presented. We show that this approach produces more non-holomorphic solutions than those obtained in previous approaches. We study the $\mathbb{C}P^2$ model in detail and present its solutions in an explicit form. We also show how to generalise this construction to $N>3$.