Constructing Carrollian field theories from null reduction

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 hypersurface. We focus on free scalar field theory and electromagnetic field theory, and show that the electric sectors and the magnetic sectors of these theories originate from different Bargmann invariant actions in one higher dimension. In the cases of massless free scalar field and d = 4 electromagnetic field, we verify the Carrollian conformal invariance of the resulting theories, and find that there appear naturally chain representations and staggered modules of Carrollian conformal algebra.