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Solving formally the auxiliary system of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> nonlinear sigma model
We show that the integrability of the $SO(N)/SO(N\ensuremath{-}1)$ 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 …