Dynamical Realization of Carrollian Conformal Symmetry and Celestial Holography Indications through Deformed Light-Cone Null Reduction

TL;DR

This paper explores Carrollian conformal symmetry through deformed light-cone reduction, deriving algebraic structures, and connecting to celestial holography by rederiving the Soft Photon Theorem and discussing holographic limitations.

Contribution

It introduces a novel approach using deformed light-cone null reduction to analyze Carrollian theories and their holographic properties, including derivation of symmetry generators and holographic breakdown mechanisms.

Findings

Carrollian vector fields decouple into scalar fields after null reduction

Energy-momentum tensor degrades from Lorentzian to Carrollian symmetry

Re-derivation of Weinberg's Soft Photon Theorem via celestial holography

Abstract

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 $c\rightarrow 0$, 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. As expected, the resulting generators produce the known kinematic Carrollian conformal algebraic commutation relations. Furthermore, leveraging the $U(1)$ global symmetry of the Carrollian theory, we rederive Weinberg's famous leading Soft Photon Theorem via celestial holography. In the end, based on the celestial holographic dictionary, we discuss the holographic properties of our Carrollian theory and identify three distinct limitations, revealing the mechanism of holographic breakdown in the non-interacting limit. Our analysis deepens the understanding of the holographic properties of Carrollian theories realized via deformed light-cone null reduction, laying the foundation for the further development of this methodology.