Superforms and the $\mathbb{C}P^{N-1}$ supersymmetric sigma model

TL;DR

This paper characterizes Maurer-Cartan superforms in the supersymmetric $ ext{CP}^{N-1}$ sigma model, solves the spectral problem, and describes an integrable system for $su(N)$-valued maps, advancing understanding of supersymmetric integrable models.

Contribution

It provides a new characterization of Maurer-Cartan superforms and links them to integrable systems in the supersymmetric $ ext{CP}^{N-1}$ sigma model.

Findings

Characterization of Maurer-Cartan 1-superforms

Solution of the linear spectral problem

Description of an integrable system for $su(N)$-valued maps

Abstract

We present a characterisation of Maurer-Cartan 1-superforms associated to the two-dimensional supersymmetric $\mathbb{C}P^{N-1}$ sigma model. We, then, solve the associated linear spectral problem and use its solutions to describe an integrable system for a $su(N)$-valued map.