Tachyons in the Galilean limit

TL;DR

This work shows that the massless Galilean particle with colour $k$ and spin $s$ emerges as the Galilean (non-relativistic) limit of a relativistic tachyon with imaginary mass $m = i k/c$, clarifying why the p=0 Galilean limit of relativistic particles is different from the Galilean limit of tachyons. The authors compare this tachyonic origin with the Galilean limits of the Nambu-Goto string and the Green-Schwarz superstring, using Souriau's 2-form framework to track spin via the Pauli-Lubanski construction. They demonstrate that tachyonic origins can yield unitary representations in the Poincaré context but lead to subtleties in supersymmetric extensions, while the Galilean superstring remains consistent due to intrinsic topological charges. The discussion suggests a broader landscape of massless Galilean systems, including dualities with Carroll limits and higher-derivative models, highlighting the nuanced role of tachyons in non-relativistic limits.

Abstract

The Souriau massless Galilean particle of "colour" $k$ and spin $s$ is shown to be the Galilean limit of the Souriau tachyon of mass $m = ik$ and spin $s$. We compare and contrast this result with the recent Galilean limit of the Nambu-Goto string and the Green-Schwarz superstring.