A note on rectangular partially massless fields

TL;DR

This paper explores non-unitary representations of so(2,d) related to higher-spin partially massless fields, revealing their branching properties and tensor products, especially in four dimensions, to understand their structure and potential as higher-spin singletons.

Contribution

It introduces a new class of non-unitary so(2,d) modules for even d, generalizing properties of higher-spin singletons and analyzing their branching and tensor product structures.

Findings

Representations branch into partially massless fields of various depths upon restriction.

Tensor products in four dimensions reveal mixed-symmetry partially massless fields.

The class of modules obeys properties similar to unitary higher-spin singletons.

Abstract

We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2,d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2,d-1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d=4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.