Carroll Fermions

TL;DR

This paper introduces two types of Carroll fermions derived from relativistic Dirac fermions through specific limits, constructs their actions, and explores their coupling to Carroll gravity across various dimensions.

Contribution

It defines electric and magnetic Carroll fermions, provides action principles for them, and investigates their interactions with Carroll gravity in different formulations.

Findings

Magnetic Carroll fermions form reducible but indecomposable representations.

An action principle for a minimal magnetic Carroll fermion is established in even dimensions.

Coupling of Carroll fermions to Carroll gravity is demonstrated in both first- and second-order formulations.

Abstract

Using carefully chosen projections, we consider different Carroll limits of relativistic Dirac fermions in any spacetime dimensions. These limits define Carroll fermions of two types: electric and magnetic. The latter type transforms as a reducible but indecomposable representation of the Carroll group. We also build action principles for all Carroll fermions we introduce; in particular, in even dimensions we provide an action principle for a minimal magnetic Carroll fermion, having the same number of components as a Dirac spinor. We then explore the coupling of these fermions to magnetic Carroll gravity in both its first-order and second-order formulations.