Algebra of Lax Connection for T-Dual Models

Abstract

We study relation between T-duality and integrability. We develop the Hamiltonian formalism for principal chiral model on general group manifold and on its T-dual image. We calculate the Poisson bracket of Lax connections in T-dual model and we show that they are non-local as opposite to the Poisson brackets of Lax connection in original model. We demonstrate these calculations on two specific examples: Sigma model on S(2) and sigma model on AdS(2).

24 pages, references added

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