Null reduction and dynamical realization of Carrollian conformal symmetries

TL;DR

The paper addresses how to realize Carrollian conformal symmetry starting from a Lorentzian, conformally invariant action. It places the theory in a deformed light-cone background, performs null reduction, and identifies the time direction with $x^+=c\tau$, then takes the Carrollian limit $c\to0$, deriving a Carrollian action $S_{\mathrm{Carroll}}$ for a complex scalar field. A dynamical construction of Carrollian conformal generators from the light-cone stress tensor, followed by dimensional reduction and the Carroll limit, yields generators such as $\tilde{H}$, $\tilde{P}^i$, $\tilde{M}^{ij}$, $\tilde{D}$, and $\tilde{K}^\mu$ that satisfy the Carrollian conformal algebra, including abelian boosts $[\tilde{M}^{i\tau},\tilde{M}^{j\tau}]=0$ and the key SCT/ dilatation commutators. The work provides a fully dynamical framework for Carrollian CFTs, clarifying light-cone definitions and demonstrating consistency with Carrollian kinematics, thereby enabling systematic studies of non-Lorentzian limits in quantum field theory.

Abstract

We start from a Lorentzian action in a deformed light-cone background and applying the method of null reduction leads to a Carrollian action in one lower spacetime dimensions. We also identify the correct light-cone definitions of the symmetry generators and their dynamical forms in terms of the fields and take the $c\rightarrow0$ limit. It is observed that these generators produce the known kinematic Carrollian conformal algebraic commutation relations.