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 nonlinear field equation remains second order in derivative. To achieve this, we introduce two novel tools. First, we generalize the bosonic map between the Galilei and Carroll algebras to include supersymmetry by using a spinor basis for the symmetry generators. We then show that Carroll superalgebras are naturally connected to Euclidean, rather than Poincaré, superalgebras. Using the real multiplet of the three-dimensional <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>1</a:mn></a:math> Euclidean supersymmetry, we construct the scalar multiplet for <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="script">N</d:mi><d:mo>=</d:mo><d:mn>2</d:mn></d:math> 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.