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

TL;DR

This work investigates the Carrollian realization of conformal symmetry by applying a deformed light-cone null reduction to a conformally invariant complex vector field and then taking the Carrollian limit $c \to 0$. The reduction yields a decoupling into independent complex scalar sectors, with the $+$ null-direction vanishing, and a Carrollian action that serves as the basis for constructing dynamical generators. The authors perform two consistent derivations of these generators: directly from the Carrollian action and via a secondary-constraint-based reduction from the parent Lorentzian theory, demonstrating agreement between approaches. The resulting Carrollian conformal algebra is shown to close with the expected relations, extending the applicability of the deformed light-cone reduction to Carrollian conformal symmetry and suggesting further applications to other CCS theories.

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.