Supersymmetric Twisted Carroll Theories

Abstract

We study the recently discussed $2+1$-dimensional Hull-type twisted $\mathcal{N}=2$ Carroll superalgebra. This structure admits both electric- and magnetic-type realizations at the level of the supersymmetry transformations. At the Lagrangian level, magnetic Carroll theories describe fields that propagate in space while remaining constrained in time, and vice versa for electric theories. We first realize this symmetry algebra through the dimensional reduction of a $2+2$-dimensional $\mathcal{N}=(1,1)$ parent algebra, originally discussed in the context of self-dual supergravity. We further find that a consistent reduction of this higher-dimensional algebra admits infinite-dimensional lifts to left- and right-chiral super-$\mathrm{BMS}_4$-type algebras, which can be combined by restoring the $R$-symmetry, leading to the type I-I magnetic super-$\mathrm{BMS}_4$ algebra. We then consistently construct magnetic off-shell scalar and Abelian Yang--Mills theories and comment on on-shell theories. Finally, in the appendix, we explain how an ordinary supersymmetric theory can be analytically continued to its twisted counterpart.