On the Non-Relativistic Expansion of Closed Bosonic Strings

TL;DR

This paper introduces a new method for deriving non-relativistic string theory by expanding the relativistic string action in powers of 1/c, avoiding complex background limits, and confirms its validity through spectrum calculations.

Contribution

It presents a novel 1/c^2 expansion approach to non-relativistic string theory that does not require near-critical background limits, aligning with known models.

Findings

Reproduces the non-relativistic string action without near-critical backgrounds.

Derives the string spectrum in flat space matching the Gomis-Ooguri model.

Provides a systematic expansion method for non-relativistic string theories.

Abstract

We develop a novel approach to non-relativistic closed bosonic string theory that is based on a string $1/c^2$ expansion of the relativistic string, where $c$ is the speed of light. This approach has the benefit that one does not need to take a limit of a string in a near-critical Kalb-Ramond background. The $1/c^2$-expanded Polyakov action at next-to-leading order reproduces the known action of non-relativistic string theory provided that the target space obeys an appropriate foliation constraint. We compute the spectrum in a flat target space, with one circle direction that is wound by the string, up to next-to-leading order and show that it reproduces the spectrum of the Gomis-Ooguri string.