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The Carrollian Superplane and Supersymmetry

Andrew James Bruce

Abstract

This note provides an intrinsic construction of the Carrollian superplane $Π\mathbb{S}\simeq \mathbb{R}^{2|4}$ 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 Inönü--Wigner contraction of a Poincaré superalgebra

The Carrollian Superplane and Supersymmetry

Abstract

This note provides an intrinsic construction of the Carrollian superplane as a supermanifold generalisation of the Carrollian plane. Moving away from the limit of relativistic spinors, we define Carroll spinors as sections of a degenerate Clifford module. We show that the Carrollian superplane is a principal -bundle. Once clock forms and a complementary basic one-form are specified, there is a pair of odd vector fields that generate novel Carrollian supersymmetry transformations, not all of which come from an Inönü--Wigner contraction of a Poincaré superalgebra
Paper Structure (9 sections, 47 equations)

This paper contains 9 sections, 47 equations.

Table of Contents

  1. Introduction
  2. The Carroll Plane and Carroll Superplane
  3. The Canonical Carrollian Geometry of the Plane
  4. The Carroll--Clifford Algebra
  5. Carroll--Clifford Modules
  6. The Carrollian superplane
  7. Connections and Clock Forms
  8. Geometric Supersymmetry
  9. Concluding Remarks