Algebra of Lax Connection for T-Dual Models

TL;DR

This paper explores how T-duality affects the integrability of principal chiral models by analyzing the Poisson brackets of Lax connections, revealing non-locality in T-dual models through explicit examples.

Contribution

It develops a Hamiltonian formalism for principal chiral models and calculates the Poisson brackets of Lax connections in T-dual models, showing their non-local nature.

Findings

Poisson brackets of Lax connections become non-local after T-duality

Explicit calculations on S(2) and AdS(2) models demonstrate the non-locality

T-duality alters the algebraic structure of integrable 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).