Dynamical Realization of Carrollian Conformal Symmetry through Deformed Light-Cone Null Reduction of Complex Vector Field Theory

Abstract: Inspired by Banerjee et al.(2018)[1] and Saha et al. (2025) [2], we utilize the deformed light-cone formalism to investigate the Carrollian version of a complex vector field theory. We find that after applying the null-reduction procedure and the Carrollian limit c $\to$ 0, the "-" null-direction and spatial components of the parent vector field decouple completely into independent scalar fields, while the "+" null-direction component vanishes. We carefully derive and demonstrate the process by which the energy-momentum tensor degrades from the Lorentzian symmetry case to the non-relativistic scenario, and point out that the secondary constraint of the original parent theory will play a crucial role in the derivation of the Carrollian generators. Finally, as expected, the resulting generators produce the known kinematic Carrollian conformal algebraic commutation relations. This work represents an extension of the application of the deformed light-cone null reduction formalism.