Current Algebra and Integrability of Principal Chiral Model on the World-sheet with General Metric

Abstract

We study the classical current algebra for principial chiral model defined on two dimensional world-sheet with general metric. We develop the Hamiltonian formalism and determine the form of the Poisson brackets between currents. Then we determine the Poisson bracket for Lax connection and we show that this Possion bracket does not depend on the world-sheet metric. We also study the Nambu-Gotto form of this model. We prove an existence of the Lax connection and determine their Poisson bracket.

arXiv comment19 pages, corrected typos

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Cited by in corpus (7)

• The classical R-matrix of AdS/CFT and its Lie dialgebra structure
• Quantum integrability and functional equations
• Hamiltonian dynamics and the hidden symmetries of the AdS_5 x S^5 superstring
• The U(N) chiral model and exact multi-solitons
• Note About Integrability and Gauge Fixing for Bosonic String on AdS(5)xS(5)
• Reduced Sigma-Model on O(N): Hamiltonian Analysis and Poisson Bracket of Lax Connection
• Integrated Lax Formalism for PCM