# (m,n)-String and D1-Brane in Stringy Newton-Cartan Background

## TL;DR

This paper investigates the behavior of (m,n)-strings and D1-branes within stringy Newton-Cartan backgrounds, deriving conditions for consistency and exploring their dynamics in this non-relativistic limit.

## Contribution

It introduces a limiting procedure to derive stringy Newton-Cartan gravity from general backgrounds and analyzes the conditions for consistent (m,n)-string and D1-brane theories.

## Key findings

- Derived Hamiltonian constraint for (m,n)-string in general backgrounds.
- Established conditions for background fields to define consistent world-sheet theories.
- Analyzed D1-brane dynamics with electric field in stringy Newton-Cartan gravity.

## Abstract

This paper is devoted to the analysis of (m,n)-string in stringy Newton-Cartan background. We start with the Hamiltonian constraint for (m,n)-string in general background and perform limiting procedure on metric and NSNS and Ramond-Ramond two form background that leads to stringy Newton-Cartan gravity. We also analyze conditions that these background fields have to obey in order to define consistent world-sheet (m,n)-theory. We also discuss D1-brane with dynamical electric field in stringy Newton-Cartan gravity.