D-dimensional massless particle with extended gauge invariance

TL;DR

This paper introduces a model for D-dimensional massless particles with extended gauge invariance, characterized by extrinsic curvature and specific geometric constraints, describing massless particles with multiple equal helicities.

Contribution

It formulates a new D-dimensional massless particle model with extended gauge symmetry based on extrinsic curvature, and characterizes its classical trajectories and quantum representations.

Findings

Classical trajectories are space-like curves satisfying specific curvature conditions.

The model is consistent on anti-de Sitter space.

Solutions correspond to massless irreducible Poincaré representations with multiple equal helicities.

Abstract

We propose the model of $D-$dimensional massless particle whose Lagrangian is given by the $N-$th extrinsic curvature of world-line. The system has $N+1$ gauge degrees of freedom constituting $W-$like algebra; the classical trajectories of the model are space-like curves which obey the conditions $k_{N+a}=k_{N-a}$, $k_{2N}=0$, $a=1,...,N-1$, $N\leq[(D-2)/2]$, while the first $N$ curvatures $k_i$ remain arbitrary. We show that the model admits consistent formulation on the anti-De Sitter space. The solutions of the system are the massless irreducible representations of Poincar\'e group with $N$ nonzero helicities, which are equal to each other.