# Relating non-relativistic string theories

## TL;DR

This paper explores different constructions of non-relativistic string theories, demonstrating their equivalence under certain conditions and analyzing a special limit relevant to AdS/CFT, revealing insights into their spectra and worldsheet dynamics.

## Contribution

It establishes the equivalence of null reduction and large speed of light expansion approaches for non-relativistic strings with an isometry, and studies a special non-relativistic limit related to Spin Matrix Theory.

## Key findings

- Non-relativistic string theories are equivalent if the longitudinal direction is an isometry.
- Theories have well-defined spectra only with nonzero winding along a spatial direction.
- A special limit leads to a non-relativistic worldsheet theory with vanishing dilaton coupling.

## Abstract

Non-relativistic string theories promise to provide simpler theories of quantum gravity as well as tractable limits of the AdS/CFT correspondence. However, several apparently distinct non-relativistic string theories have been constructed. In particular, one approach is to reduce a relativistic string along a null isometry in target space. Another method is to perform an appropriate large speed of light expansion of a relativistic string. Both of the resulting non-relativistic string theories only have a well-defined spectrum if they have nonzero winding along a longitudinal spatial direction. In the presence of a Kalb--Ramond field, we show that these theories are equivalent provided the latter direction is an isometry. Finally, we consider a further limit of non-relativistic string theory that has proven useful in the context of AdS/CFT (related to Spin Matrix Theory). In that case, the worldsheet theory itself becomes non-relativistic and the dilaton coupling vanishes.