Longitudinal Galilean and Carrollian limits of non-relativistic strings

TL;DR

This paper explores two novel non-Lorentzian limits of non-relativistic strings, resulting in Galilean and Carrollian worldsheet structures, and analyzes their formulations and specific target space geometries.

Contribution

It introduces a new Carrollian string limit and systematically studies both Galilean and Carrollian non-Lorentzian string theories, extending previous work on non-relativistic strings.

Findings

Derived Nambu-Goto and Polyakov actions for both limits.

Identified gauge fixing choices for the new limits.

Analyzed the Galilean string in specific target space geometries.

Abstract

It is well known that one can take an infinite speed of light limit that gives rise to non-relativistic strings with a relativistic worldsheet sigma model but with a non-relativistic target space geometry. In this work we systematically explore two further limits in which the worldsheet becomes non-Lorentzian. The first gives rise to a Galilean string with a Galilean structure on the worldsheet, extending previous work on Spin Matrix-related string theory limits. The second is a completely novel limit leading to a worldsheet theory with a Carrollian structure. We find the Nambu-Goto and Polyakov formulations of both limits and explore gauge fixing choices. Furthermore, we study in detail the case of the Galilean string for a class of target space geometries that are related to Spin Matrix target space geometries, for which the Nambu-Goto action (in static gauge) is quadratic in the fields.