Constructing Carrollian Field Theories from Null Reduction

TL;DR

This paper introduces a method to derive $d$-dimensional Carrollian field theories from null reductions of $(d+1)$-dimensional Bargmann invariant actions, revealing new structures and conformal invariance properties.

Contribution

It presents a novel approach to construct off-shell Carrollian theories via null reduction, highlighting the origin of electric and magnetic sectors from higher-dimensional actions.

Findings

Electric and magnetic sectors originate from different higher-dimensional actions.

Carrollian conformal invariance is verified for specific cases.

Chain representations and staggered modules of Carrollian conformal algebra are identified.

Abstract

In this paper, we propose a novel way to construct off-shell actions of $d$-dimensional Carrollian field theories by considering the null-reduction of the Bargmann invariant actions in $d+1$ dimensions. This is based on the fact that $d$-dimensional Carrollian symmetry is the restriction of the $(d+1)$-dimensional Bargmann symmetry to a null hyper-surface. We focus on free scalar field theory and electromagnetic field theory, and show that the electric and magnetic sectors of these theories originate from different Bargmann invariant actions in one higher dimension. In the cases of the massless free scalar field and $d=4$ electromagnetic field, we verify Carrollian conformal invariance of the resulting theories, and find that there appear naturally chain representations and staggered modules of Carrollian conformal algebra.