Schrodinger Sigma Models and Jordanian Twists

TL;DR

This paper explores the integrable structures of two-dimensional sigma models on Schrödinger spacetimes, revealing a Jordanian deformation of Yangian symmetry through gauge transformations and twists.

Contribution

It demonstrates the equivalence of anisotropic and isotropic Lax pairs via non-local gauge transformations and uncovers a Jordanian deformation of Yangian symmetry in these models.

Findings

Anisotropic Lax pairs are equivalent to isotropic ones under non-local gauge transformations.

A Jordanian twist relates gauge transformations to deformed Yangian symmetry.

Identification of an exotic symmetry as a Jordanian deformation of Y(sl(2)).

Abstract

We proceed to study the integrable structures of two-dimensional non-linear sigma models defined on three-dimensional Schrodinger spacetimes. We show that anisotropic Lax pairs are equivalent with isotropic Lax pairs with flat conserved currents under non-local gauge transformations. Then a quite non-trivial realization of the undeformed Yangian symmetry Y(sl(2)) is revealed after an appropriate gauge fixing, which is determined by comparing the gauge transformation to a quantum Jordanian twist. As a result, an exotic symmetry found in arXiv:1209.4147 may be interpreted as a Jordanian deformation of Y(sl(2)).