Solving formally the auxiliary system of O(N) nonlinear sigma model

We show that the integrability of the SO(N)/SO(N - 1) principal chiral model (PCM) originates from the Pohlmeyer reduction of the O(N) nonlinear sigma model (NLSM). In particular, we show that the Lax pair of the PCM is related upon redefinitions and identification of parameters to the zero curvature condition, which is a consequence of the flatness of the enhanced space used in the Pohlmeyer reduction. This identification provides the solution of the auxiliary system that corresponds to an arbitrary NLSM/PCM solution.

Automated summary

We demonstrate that the integrability of the SO(N)/SO(N - 1) principal chiral model (PCM) originates from the Pohlmeyer reduction of the O(N) nonlinear sigma model (NLSM). Specifically, we show that the Lax pair of the PCM can be related to the zero curvature condition through redefinitions and identification of parameters, which arises from the flatness of the enhanced space used in the Pohlmeyer reduction. This identification provides a solution for the auxiliary system corresponding to any NLSM/PCM solution.