The Carrollian Superplane and Supersymmetry

TL;DR

This paper constructs the Carrollian superplane as a supermanifold, introduces Carroll spinors via degenerate Clifford modules, and reveals new N=2 Carrollian supersymmetry transformations that differ from relativistic limits.

Contribution

It provides an intrinsic supermanifold construction of the Carrollian superplane and identifies novel supersymmetry transformations not derived from Poincaré contraction.

Findings

Carrollian superplane modeled as a supermanifold.

Definition of Carroll spinors as sections of degenerate Clifford modules.

Discovery of new N=2 Carrollian supersymmetry transformations.

Abstract

This note provides an intrinsic construction of the Carrollian superplane $\Pi \mathbb{S}\simeq \mathbb{R}^{2|4}$ as a supermanifold generalisation of the Carrollian plane. Moving away from the $c\rightarrow 0$ limit of relativistic spinors, we define Carroll spinors as sections of a degenerate Clifford module. We show that the Carrollian superplane is a principal $\mathbb{R}^{1|2}$-bundle. Once clock forms and a complementary basic one-form are specified, there is a pair of odd vector fields that generate novel $N =2$ Carrollian supersymmetry transformations, not all of which come from an In\"on\"u--Wigner contraction of a Poincar\'e superalgebra