An infinite supermultiplet of massive higher-spin fields

TL;DR

This paper revisits Majorana's infinite-component wave equation, revealing its solutions form supermultiplets of the superPoincare algebra, and constructs an infinite supermultiplet of massive fields of all spins in four dimensions.

Contribution

It generalizes Majorana's equation to arbitrary dimensions and Regge trajectories, and constructs an infinite supermultiplet of massive fields with a novel group-theoretic structure.

Findings

Massless solutions form supermultiplets with tensorial central charges.

Infinite supermultiplet of all spins with equal mass is constructed.

The supermultiplet carries an irreducible representation of OSp(1|4) and superPoincare groups.

Abstract

The representation theory underlying the infinite-component relativistic wave equation written by Majorana is revisited from a modern perspective. On the one hand, the massless solutions of this equation are shown to form a supermultiplet of the superPoincare algebra with tensorial central charges; it can also be obtained as the infinite spin limit of massive solutions. On the other hand, the Majorana equation is generalized for any space-time dimension and for arbitrary Regge trajectories. Inspired from these results, an infinite supermultiplet of massive fields of all spins and of equal mass is constructed in four dimensions and proved to carry an irreducible representation of the orthosymplectic group OSp(1|4) and of the superPoincare group with tensorial charges.