Solving formally the Auxiliary System of $O(N)$ Non Linear Sigma Model

Abstract

We show that the integrability of the $SO(N)/SO(N-1)$ Principal Chiral Model (PCM) originates from the Pohlmeyer reduction of the $O(N)$ Non Linear 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.

arXiv comment5 pages, v2 minor changes to match published version

References in corpus (14)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Type IIB superstring action in AdS_5 x S^5 background
• The Algebraic Curve of Classical Superstrings on AdS_5xS^5
• Algebraic Curve for the SO(6) sector of AdS/CFT
• Lagrangian Formulation of Symmetric Space sine-Gordon Models
• Pohlmeyer reduction revisited
• Magnons, their Solitonic Avatars and the Pohlmeyer Reduction
• Towards Lefschetz thimbles in Sigma models, I
• Dressed Elliptic String Solutions on RxS^2
• Salient Features of Dressed Elliptic String Solutions on $\mathbb{R}\times$S${}^2$
• Stability Analysis of Classical String Solutions and the Dressing Method
• The Dressing Method as Non Linear Superposition in Sigma Models
• Dressed Minimal Surfaces in AdS${}_4$

Cited by in corpus (1)

• Novel aspects of integrability for NLSMs in symmetric spaces