Coset space actions for nonrelativistic strings

TL;DR

This paper develops coset space models for nonrelativistic strings in flat space and AdS$_5\times$S$^5$, providing a Lax representation and highlighting differences from relativistic models.

Contribution

It introduces coset formulations for nonrelativistic string limits based on specific algebras, offering a new approach to their integrability.

Findings

Constructed coset models for nonrelativistic strings

Derived Lax pairs for equations of motion

Identified differences from relativistic string formulations

Abstract

We formulate the stringy nonrelativistic limits of the flat space and AdS$_5\times$S$^5$ string as coset models, based on the string Bargmann and extended string Newton-Hooke algebras respectively. Our construction mimics the typical relativistic one, but differs in several interesting ways. Using our coset formulation we give a Lax representation of the equations of motion of both models.