Some properties of classical solutions in Grassmannian sigma models
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.
scientific article; zbMATH DE number 3844702