Sergeev, Armen Grassmannian sigma-models. (English) Zbl 1143.81020 J. Geom. Symmetry Phys. 9, 45-65 (2007). Summary: We study solutions of Grassmannian sigma-model both in finite-dimensional and infinite-dimensional settings. Mathematically, such solutions are described by harmonic maps from the Riemann sphere \(\mathbb C\mathbb P^1\) or, more generally, compact Riemann surfaces to Grassmannians. We describe first how to construct harmonic maps from compact Riemann surfaces to the Grassmann manifold \(G_r(\mathbb C^d)\), using the twistor approach. Then we switch to the infinite-dimensional setting and consider harmonic maps from compact Riemann surfaces to the Hilbert-Schmidt Grassmannian \(\text{Gr}_{\text{HS}}(H)\) of a complex Hilbert space \(H\). Solutions of this infinite-dimensional sigma-model are, conjecturally, related to Yang-Mills fields on \(\mathbb R^4\). Cited in 1 Document MSC: 81T10 Model quantum field theories 81T13 Yang-Mills and other gauge theories in quantum field theory 51M35 Synthetic treatment of fundamental manifolds in projective geometries (Grassmannians, Veronesians and their generalizations) 14M15 Grassmannians, Schubert varieties, flag manifolds PDFBibTeX XMLCite \textit{A. Sergeev}, J. Geom. Symmetry Phys. 9, 45--65 (2007; Zbl 1143.81020)