Phys.Rev.D, 111, 085008 (2025)

Supersymmetric Carroll Galileons in three dimensions

Utku Zorba¹, Ilayda Bulunur², Oguzhan Kasikci², Mehmet Ozkan², Y.Pang³and Mustafa Salih Zog²

1 Department Of Engineering Sciences, Istanbul University-Cerrahpasa, Avcilar 34320 Istanbul, Türkiye.

2 Department of Physics, Istanbul Technical University, Maslak 34469 Istanbul, Türkiye.

3 Center for Joint Quantum Studies and Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.

* pangyi1@dgquanwei.com, zog@itu.edu.tr

Abstract

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 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.