Carroll theories from Lorentzian light-cone theories

TL;DR

This paper develops Carrollian field theories by null reduction from Lorentzian light-cone actions, revealing new structures and constraints, and clarifying the relation between higher-dimensional Lorentzian theories and lower-dimensional Carrollian dynamics.

Contribution

It introduces a deformation of light-cone actions to derive both magnetic and electric Carroll theories, eliminating second-class constraints and clarifying solution truncations.

Findings

Magnetic Carroll theories can be directly derived from Lorentzian actions.

Deformation is essential for obtaining electric Carroll theories.

Magnetic Carroll solutions represent a truncation of higher-dimensional Lorentzian solutions.

Abstract

We derive Carrollian field theories via null reduction from Lorentzian light-cone actions in Minkowski spacetime. By suitably deforming the light-cone action, we reduce the Poincar\'e invariance to a Bargmann subgroup, from which both magnetic and electric Carroll actions can be obtained in one lower dimension. Through a canonical analysis, we show that the second-class constraints usually found in Lorentzian light-cone theories are absent for these deformed Bargmann-invariant actions. We demonstrate the procedure for theories with and without gauge symmetry. Notably, while the magnetic Carroll sector can be directly derived from the original Lorentzian action, the deformation is essential to obtain the electric Carroll sector. We further argue that magnetic Carroll solutions in $d$ dimensions represent a consistent truncation of the solutions of the $(d+1)$-dimensional Lorentzian parent theory, providing an effective description of light-cone dynamics near a null hypersurface. For gauge theories, we also highlight the role of the light-cone gauge condition in deriving Carrollian theories.