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We obtained the formal solution of the auxiliary system of Non Linear SigmaModels, whose target space is a rank 1 symmetric space based on the indefiniteorthogonal group O(p,q), corresponding to an arbitrary solution of the NLSM.This class includes Anti-de Sitter, de Sitter and Hyperbolic spaces, which areof interest in view of the AdS/CFT correspondence. The formal solution isrelated to the Pohlmeyer reduction of the NLSM, constituting another linkbetween the NLSM and the reduced theory. Besides deriving the solution, we alsoreview the Pohlmeyer reduction of such models. Finally, we comment on theimplications for the monodromy matrix and its eigenvalues.

Novel aspects of integrability for NLSMs in symmetric spaces