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

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