On massive spin-3/2 in the Fradkin-Vasiliev formalism

TL;DR

This paper examines the gauge-invariant description of massive spin-3/2 fields in the Fradkin-Vasiliev formalism, demonstrating how general properties manifest and exploring the effects of massless fields on interaction vertices.

Contribution

It shows how the general properties of gauge-invariant vertices are realized in the Fradkin-Vasiliev formalism for massive spin-3/2 fields, including the impact of massless fields on vertex equivalence.

Findings

Existence of enough field redefinitions to simplify vertices into abelian form.

Presence of two abelian vertices not equivalent on-shell to trivially gauge invariant ones.

Identification of a vertex reproducing minimal interaction for massive spin-3/2.

Abstract

One of the possible approaches to the construction of massive higher spin interactions is to use their gauge invariant description based on the introduction of the appropriate set of Stueckelberg fields. Recently, the general properties of such approach were investigated in [1]. The main findings of this work can be formulated in two statements. At first, there always exist enough field redefinitions to bring the vertex into abelian form where there are some corrections to the gauge transformations but the gauge algebra is undeformed. At second, with the further (as a rule higher derivative) field redefinitions one can bring the vertex into trivially gauge invariant form expressed in terms of the gauge invariant objects of the free theory. Our aim in this work is to show (using a simple example) how these general properties are realised in the so-called Fradkin-Vasiliev formalism and to see the effects (if any) that the presence of massless field, and hence of some unbroken gauge symmetries, can produce. As such example we take the gravitational interaction for massive spin-3/2 field so we complete the investigation started in [2] relaxing all restrictions on the number of derivatives and allowed field redefinitions. We show that in spite of the presence of massless spin-2 field, the first statement is still valid, while there exist two abelian vertices which are not equivalent on-shell to the trivially gauge invariant ones. Moreover, it is one of this abelian vertices that reproduce the minimal interaction for massive spin-3/2.