Some properties of classical solutions in Grassmannian sigma models
type: Item
instance of: scholarly article
title: Some properties of classical solutions in Grassmannian sigma models
zbMATH Open document ID: 0532.58035
DOI: 10.1007/BF00402250
author: A. M. Din
author: Wojciech J. Zakrzewski
published in: Letters in Mathematical Physics
publication date: 1983-01-01T00:00:00Z
review text: The Grassmannian sigma models G(M,N) are known to have two classes of classical solutions, the generic and the special ones. They depend on M respectively \(M'<M\) holomorphic vectors and generalize in a natural way the classification of solutions in the \(CP^{N-1}\) model \((M=1)\). In contradistinction to this special case there exists as yet no completeness proof of the classification. The topological charge and the action are shown to be given by simple expressions involving the degree of polynomials which resemble the \(CP^{N-1}\) results. The supersymmetric Dirac equation with a given solution background can also be solved and the solutions are found to be related to the solutions of the associated Riemann-Hilbert problem. The number of independent solutions of either chirality can be counted and the index theorem is seen to be satisfied in a non-minimal way.
Mathematics Subject Classification ID: 58J90
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 81T60
zbMATH DE Number: 3844702
zbMATH Keywords: instanton
zbMATH Keywords: supersymmetric Dirac equation
zbMATH Keywords: Riemann-Hilbert problem
MaRDI profile type: Publication
cites work: Classical solutions in Grassmannian sigma-models
full work available at URL: https://doi.org/10.1007/bf00402250
OpenAlex ID: W1975575225
description: scientific article; zbMATH DE number 3844702