Poisson-Lie T-duals of the bi-Yang-Baxter models

TL;DR

This paper proves that certain analytic continuations of Poisson-Lie T-duals of bi-Yang-Baxter models match generalized lambda models, and extends this to a broader class of sigma models, revealing deep dualities in integrable systems.

Contribution

It establishes a new connection between Poisson-Lie T-duals and generalized lambda models, generalizing previous results to universal WZW-type sigma models.

Findings

Analytic continuation of Poisson-Lie T-duals matches generalized lambda models.

Generalization to universal WZW-type sigma models and Poisson-Lie symmetric models.

Deepens understanding of dualities in integrable sigma models.

Abstract

We prove the conjecture of Sfetsos, Siampos and Thompson that suitable analytic continuations of the Poisson-Lie T-duals of the bi-Yang-Baxter sigma models coincide with the recently introduced generalized lambda models. We then generalize this result by showing that the analytic continuation of a generic sigma model of "universal WZW-type" introduced by Tseytlin in 1993 is nothing but the Poisson-Lie T-dual of a generic Poisson-Lie symmetric sigma model introduced by Klimcik and Severa in 1995.