A Twisted Origin for Magnetic Carroll Supersymmetry

TL;DR

This paper reveals that magnetic Carroll supersymmetry originates from a twisted relativistic algebra, constructing a 3D ${\mathcal{N}}=2$ model that connects to super-BMS$_4$ symmetries and flat-space holography.

Contribution

It demonstrates that magnetic Carroll supersymmetry arises from a twisted relativistic parent, providing a new perspective on super-BMS$_4$ and flat-space holography.

Findings

Constructed a 3D ${\mathcal{N}}=2$ magnetic Carroll algebra with supersymmetric action.

Identified supercharges with unique algebraic properties, including one squaring to spatial momentum.

Connected the conformal extension to the global part of super-BMS$_4$ algebra.

Abstract

Magnetic Carrollian theories provide a natural setting for field theories with nontrivial spatial structure in the Carroll limit and are therefore natural candidates for flat-space holographic duals. Embedding such boundary theories into a top-down framework requires a consistent supersymmetric completion and, in particular, an understanding of the relativistic origin of magnetic Carroll supersymmetry. We show that the relevant magnetic Carroll algebra does not arise from a naive contraction of the standard relativistic supersymmetry algebra, but instead descends from a twisted relativistic parent. As an explicit realization, we construct a three-dimensional ${\mathcal{N}}=2$ magnetic Carroll algebra together with a supersymmetric vector-multiplet action. Unlike the electric case, the resulting structure contains one supercharge that squares to spatial momentum, a mixed anticommutator that yields the Hamiltonian, and a nilpotent second supercharge. We further show that its conformal extension coincides with the global part of a supersymmetric BMS$_4$ algebra. This provides a physical and relativistic origin for a super-BMS$_4$ structure recently identified by complementary algebraic methods, and strengthens the case for magnetic Carroll theories in flat-space holography and supersymmetric asymptotic symmetries.