# Lax pairs for string Newton Cartan geometry

## TL;DR

This paper demonstrates classical integrability of nonrelativistic strings in stringy Newton-Cartan geometry by constructing Lax pairs and a monodromy matrix, revealing an infinite set of conserved charges.

## Contribution

It introduces a systematic formulation of Lax pairs for nonrelativistic strings in stringy Newton-Cartan geometry, establishing their classical integrability.

## Key findings

- Classical integrability of nonrelativistic strings in stringy NC geometry.
- Construction of the monodromy matrix and non-local conserved charges.
- Establishment of a Lax pair formulation for the system.

## Abstract

In this paper, based on a systematic formulation of Lax pairs, we show \textit{classical} integrability for nonrelativistic strings propagating over \textit{stringy} Newton-Cartan (NC) geometry. We further construct the corresponding \textit{monodromy} matrix which leads to an infinite tower of \textit{non-local} conserved charges over stringy NC background.