NON-LINEAR SIGMA-MODELS OF SYMMETRIC-SPACES

Two-dimensional nonlinear models, where the fields are elements of a symmetric space, are considered. We first review the theory of symmetric spaces, in particular for the orthogonal and unitary groups. These spaces include real and complex Grassmannian manifolds, which generalize real (RPN) and complex (CPN) projective spaces, respectively. The theories are examined as N in the 1N expansion. Although the expansion for O(N) or U(N) cannot be used to calculate any correlation function of the 's, it demonstrates asymptotic freedom and the correct mass spectra for the theory. With SU(N), arguments suggest that the original representation will be confined as in the CPN model. From a nonlocal charge, a proposed two-body S matrix, representative of this class of theories, is found. The difficulties of checking the S matrix as N and s are discussed. Qualitatively, the S matrix confirms the mass spectra expected from the 1N expansion. © 1979 The American Physical Society.