Pairwise Helicity in Higher Dimensions

TL;DR

This paper extends the concept of pairwise helicity, previously studied in four dimensions, to higher-dimensional spacetimes, revealing its origin in p-form electrodynamics and its relation to brane configurations.

Contribution

It generalizes the notion of pairwise helicity to higher dimensions and interprets it as a quantum number under a specific little group for brane pairs.

Findings

Pairwise helicity originates from p-form electrodynamics with nonlocal branes.

It is characterized as an SO(2) quantum number for brane pairs.

Higher-dimensional little groups can induce multiparticle or multi-brane representations.

Abstract

Studies of scattering amplitudes for electric and magnetic charges have identified previously overlooked multiparticle representations of the Poincar\'e group in four dimensions. Such representations associate nontrivial quantum numbers (known as pairwise helicities) with asymptotically separated pairs of particles, and thus cannot be described as tensor products of one-particle states. We extend this construction to sources and spacetimes of higher dimension. We first establish the dynamical origin of pairwise helicity in $p$-form electrodynamics coupled to mutually nonlocal branes. We then interpret this pairwise helicity as a quantum number under an $SO(2)$ pairwise little group associated with pairs of distinct branes. We further characterize the "higher" little groups that could in principle be used to induce multiparticle or multi-brane representations of the Lorentz group.