Carroll spinors

TL;DR

This work analyzes Carroll spinors, arising from the $c\to 0$ contraction of Lorentzian spinor structures, and develops the Carroll--Clifford framework in both 1+1 and 4D settings. It classifies Carroll fermions into electric and magnetic sectors, derives their Lagrangians, and examines charge conjugation, parity, and the (non)existence of a meaningful Carroll chirality, culminating in a Carroll Ising CCFT$_2$ and a discussion of Carroll ELKO with SIM$(2)$-like invariances explored in Appendix B. The paper also surveys potential applications in flat-space holography, near-horizon soft hair, and condensed-matter analogues, while outlining open questions and consistency conditions such as the Bunster–Henneaux relation for Carroll theories. The introduction of Carroll ELKO and the explicit SIM$(2)$ contraction connect exotic spinor structures to broader symmetry frameworks, suggesting avenues for future exploration in holography and high-energy limits of string theory.

Abstract

This crisp summary of salient aspects of Carroll spinors is dedicated to the memory of Dharam Ahluwalia, the intrepid champion of ELKO spinors.