Supersymmetric Carroll Galileons in Three Dimensions

We present the first example of an interacting Carroll supersymmetric field theory with both temporal and spatial derivatives, belonging to the Galileon class, where the non-linear field equation remains second-order in derivative. To achieve this, we introduce two novel tools. First, we demonstrate that the two-dimensional Galilei/Carroll duality can be extended to higher dimensions, and includes the supersymmetry, by expressing the generators in a spinor basis. We then show that Carroll superalgebras are naturally connected to Euclidean, rather than Poincar\'e, superalgebras. Using the real multiplet of the three-dimensional N $=1$ Euclidean supersymmetry, we construct the scalar multiplet for N $=2$ Carroll supersymmetry and develop a tensor calculus to realize the aforementioned model. These results offer new insights into the structure of genuine higher-dimensional Carroll field theories and Carroll supersymmetry. While these tools are utilized to build a specific model, we anticipate that they possess broader applications in Carrollian physics.