Carroll fermions, expansions and the lightcone

TL;DR

This paper derives Carrollian fermion actions from relativistic Dirac theory via a systematic expansion in the speed of light, connecting intrinsic Carrollian structures with light-cone dynamics and relativistic fermions.

Contribution

It establishes a systematic derivation of Carrollian fermions from relativistic theories and links light-cone coordinates to Carrollian structures in lower dimensions.

Findings

Derived Carrollian fermion actions from relativistic Dirac theory.

Connected light-cone coordinates with Carrollian fermions in lower dimensions.

Explained features of Carrollian fermions relating to relativistic fermions in different dimensions.

Abstract

We investigate fermions on Carrollian manifolds. We complement previous intrinsic analysis by deriving Carrollian fermion actions from a relativistic Dirac theory via a systematic expansion in the speed of light ($c$). We then study relativistic fermions in light-cone coordinates and their connection to Carrollian fermions in one lower dimension. This follows from the recent observation that the Poincar\'e algebra, written in lightcone coordinates contains (two) co-dimension one Carroll sub-algebras. Our results establish a clear bridge between intrinsic Carrollian constructions, small $c$-expansion and light-cone dynamics. In the process, we understand why Carrollian fermions in $D$-dimensions have features that relate them to relativistic fermions in both $D$ and $(D+1)$ dimensions.