Field Theories on Null Manifolds

TL;DR

This paper explores the structure of field theories on null manifolds, focusing on a novel interacting conformal Carrollian scalar electrodynamics, and demonstrates its symmetry properties and conserved charges.

Contribution

It introduces the first example of an interacting conformal Carrollian field theory with a proposed action respecting Carrollian symmetries.

Findings

The equations of motion satisfy Helmholtz conditions for a Lagrangian.

The proposed action respects finite and infinite conformal Carrollian symmetries.

Conserved charges form an algebra consistent with the infinite Carrollian conformal algebra.

Abstract

We argue that generic field theories defined on null manifolds should have an emergent BMS or conformal Carrollian structure. We then focus on a simple interacting conformal Carrollian theory, viz. Carrollian scalar electrodynamics. We look at weak (on-shell) and strong invariance (off-shell) of its equations of motion under conformal Carrollian symmetries. Helmholtz conditions are necessary and sufficient conditions for a set of equations to arise from a Lagrangian. We investigate whether the equations of motion of Carrollian scalar electrodynamics satisfy these conditions. Then we proposed an action for the electric sector of the theory. This action is the first example for an interacting conformal Carrollian Field Theory. The proposed action respects the finite and infinite conformal Carrollian symmetries in d = 4. We calculate conserved charges corresponding to these finite and infinite symmetries and then rewrite the conserved charges in terms of the canonical variables. We finally compute the Poisson brackets for these charges and confirm that infinite Carrollian conformal algebra is satisfied at the level of charges.