Exotic symmetry and monodromy equivalence in Schrodinger sigma models

TL;DR

This paper explores the integrable structure of Schrodinger sigma models, revealing exotic symmetries and monodromy equivalence through algebraic and geometric analyses of conserved charges and spectral parameters.

Contribution

It demonstrates an infinite-dimensional extension of the q-deformed Poincare algebra and establishes gauge equivalence of monodromy matrices in different descriptions.

Findings

Identification of Yangian and q-deformed Poincare algebras

Construction of non-local charges via a spectral parameter map

Gauge equivalence of monodromy matrices

Abstract

We consider the classical integrable structure of two-dimensional non-linear sigma models with target space three-dimensional Schrodinger spacetimes. There are the two descriptions to describe the classical dynamics: 1) the left description based on SL(2,R)_L and 2) the right description based on U(1)_R. We have shown the sl(2,R)_L Yangian and q-deformed Poincare algebras associated with them. We proceed to argue an infinite-dimensional extension of the q-deformed Poincare algebra. The corresponding charges are constructed by using a non-local map from the flat conserved currents related to the Yangian. The exotic tower structure of the charges is revealed by directly computing the classical Poisson brackets. Then the monodromy matrices in both descriptions are shown to be gauge-equivalent via the relation between the spectral parameters. We also give a simple Riemann sphere interpretation of this equivalence.