Classical Integrability of the Squashed Three-sphere, Warped AdS3 and Schroedinger Spacetime via T-Duality

TL;DR

This paper demonstrates that certain 2D non-linear sigma models with specific target spaces are classically integrable, achieved through T-duality, and reveals an extended symmetry structure via non-local conserved charges.

Contribution

It shows how integrability of models on squashed three-sphere, warped AdS3, and Schroedinger spacetime can be established through T-duality, introducing an infinite set of conserved charges.

Findings

Constructed non-local conserved charges from T-dual Lax currents.

Extended symmetry to sl2(R)+sl2(R) in warped AdS3 and Schroedinger spacetime.

Established classical integrability of these models via T-duality.

Abstract

We discuss the integrability of 2d non-linear sigma models with target space being the squashed three-sphere, warped anti-de Sitter space and the Schroedinger spacetime. These models can be obtained via T-duality from integrable models. We construct an infinite family of non-local conserved charges from the T-dual Lax currents, enhancing the symmetry of warped anti-de Sitter space and the Schroedinger spacetime to sl2(R)+sl2(R).