Bihamiltonity as origin of T-duality of the closed string model

TL;DR

This paper explores how bihamiltonian structures in integrable string models lead to T-duality, introducing new Poisson brackets influenced by background fields, and establishing conditions for integrability and duality.

Contribution

It demonstrates that bihamiltonity underpins T-duality in closed string models and derives new background-dependent Poisson brackets.

Findings

Bihamiltonity is the origin of T-duality in string models.

New Poisson brackets depend on background fields and derivatives.

Integrability requires compatibility of bihamiltonity and Jacobi identity.

Abstract

In assumption,that string model is the integrable model for particular kind of the background fields, the closed string model in the background gravity field and the antisymmetric B-field is considered as the bihamiltonian system. It is shown, that bihamiltonity is origin of T-duality of the string models. The new Poisson brackets, depending of the background fields and of their derivatives, are obtained. The integrability condition is obtained as the compactability of the bihamoltonity condition and the Jacobi identity of the new Poisson bracket. The B-chiral string model is dual to the chiral string model for the constant background fields.