Novel aspects of integrability for nonlinear sigma models in symmetric spaces

Abstract

We obtained the formal solution of the auxiliary system of nonlinear sigma models (NLSMs), whose target space is a rank 1 symmetric space based on the indefinite orthogonal group $O(p,q)$, corresponding to an arbitrary solution of the NLSM. This class includes anti-de Sitter, de Sitter, and hyperbolic spaces, which are of interest in view of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. The formal solution is related to the Pohlmeyer reduction of the NLSM, constituting another link between the NLSM and the reduced theory. Besides deriving the solution, we also review the Pohlmeyer reduction of such models. Finally, we comment on the implications for the monodromy matrix and its eigenvalues.