Novel aspects of integrability for NLSMs in symmetric spaces

TL;DR

This paper provides a formal solution to the auxiliary system of NLSMs on symmetric spaces like AdS, linking it to Pohlmeyer reduction and discussing implications for the monodromy matrix.

Contribution

It introduces a formal solution for NLSMs on rank 1 symmetric spaces and explores its relation to Pohlmeyer reduction, expanding understanding of integrability in these models.

Findings

Derived the formal solution for the auxiliary system of NLSMs.

Established the connection between the solution and Pohlmeyer reduction.

Discussed implications for the monodromy matrix and eigenvalues.

Abstract

We obtained the formal solution of the auxiliary system of Non Linear Sigma Models, 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 AdS/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.