Super-Carrollian and Super-Galilean Field Theories

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.