The Carrollian Superplane and Supersymmetry

This note provides an intrinsic construction of the Carrollian superplane $\mathrm{\Pi }\mathbb{S}\simeq {\mathbb{R}}^{2\mathrm{\mid }4}$ as a supermanifold generalisation of the Carrollian plane. Moving away from the $c\to 0$ limit of relativistic spinors, we define Carroll spinors as sections of a degenerate Clifford module. We show that the Carrollian superplane is a principal ${\mathbb{R}}^{1\mathrm{\mid }2}$-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 Inönü–Wigner contraction of a Poincaré superalgebra