Electromagnetic helicity flux operators in higher dimensions

TL;DR

This paper constructs electromagnetic helicity flux operators in higher dimensions, revealing their algebraic structure, relation to the Poincaré group, and a topological Chern-Simons term at null infinity, extending known four-dimensional results.

Contribution

It introduces a non-Abelian group of helicity flux operators in higher dimensions and links minimal operators to massless Poincaré representations, expanding the understanding of helicity flux in higher-dimensional spacetimes.

Findings

Helicity flux operators form a non-Abelian group in higher dimensions.

Minimal helicity flux operators correspond to massless Poincaré representations.

A topological Chern-Simons term evaluates these operators at null infinity.

Abstract

The helicity flux operator is a fascinating quantity that characterizes the angular distribution of the helicity of radiative photons or gravitons and it has many interesting physical consequences. In this paper, we construct the electromagnetic helicity flux operators which form a non-Abelian group in general dimensions, among which the minimal helicity flux operators form the massless representation of the little group, a finite spin unitary irreducible representation of the Poincar\'e group. As in four dimensions, they generate an extended angle-dependent transformation on the Carrollian manifold. Interestingly, there is no known corresponding bulk duality transformation in general dimensions. However, we can construct a topological Chern-Simons term that evaluates the minimal helicity flux operators at $\mathcal{I}^+$.