General classical solutions of the complex grassmannian and CP N−1 sigma models

Abstract

General classical solutions are constructed for the complex grassmannian non-linear sigma models in two euclidean dimensions in terms of holomorphic functions. The grassmannian sigma models are a simple generalization of the well-known CP N−1 model in two dimensions and they share various interesting properties; existence of (anti-) instantons, an infinite number of conserved quantities and complete integrability.