Super-Carrollian and Super-Galilean Field Theories

TL;DR

This paper extends the study of Carroll and Galilei symmetries from scalar to fermionic and supersymmetric field theories, providing new formulations and insights into their limiting behaviors from relativistic theories.

Contribution

It introduces fermionic and supersymmetric Carrollian and Galilean field theories, including supermultiplet constructions and multiple perspectives on the limiting process.

Findings

Constructed consistent electric and magnetic descriptions of Carrollian and Galilean fermions.

Extended the framework to include $ abla=1$ off-shell supersymmetric theories in four dimensions.

Formulated supermultiplets combining scalars, fermions, and auxiliary fields under Carrollian and Galilean symmetries.

Abstract

The exploration of scalar field theories that exhibit Carroll and Galilei symmetries has attracted a lot of attention. In this paper, we generalize these studies to fermionic field theories and construct consistent electric and magnetic descriptions of Carrollian and Galilean spin $\tfrac{1}{2}$ fermions. We showcase various methods that offer complementary perspectives into the limiting process of the underlying relativistic theories. Moreover, we extend our study to $\mathcal{N}=1$ off-shell supersymmetric field theories in four dimensions. By introducing suitable Grassmann-analyticity conditions, we formulate the corresponding super-Carrollian and super-Galilean theories. These theories combine the established Carroll/Galilei scalars with the Carroll/Galilei fermions and a range of auxiliary fields into supermultiplets.