Conformal gauge theory of vector-spinors and spin-3/2 particles

TL;DR

This paper develops a conformal gauge theory for vector-spinor fields, demonstrating the absence of classical inconsistencies and analyzing the quantum properties, including anomalies and unitarity issues, of spin-3/2 particles.

Contribution

It introduces a unique off-shell fermionic gauge invariance for vector-spinor fields and clarifies the theory's consistency and quantum anomaly structure.

Findings

The theory is Weyl invariant in the massless limit.

Velo-Zwanziger instability is absent in this formulation.

The conformal anomaly's $a$ charge is negative, indicating nonunitarity.

Abstract

The unique off-shell fermionic gauge invariance of a vector-spinor field theory is found, and the invariant action is derived. The latter is Weyl invariant in any dimension in the massless limit, and it coincides with the singular point of the one-parameter family of Rarita-Schwinger Lagrangians, in agreement with previous findings in flat space. Pure gauge configurations are represented by gamma-trace vector-spinors, which can be gauged away in a global fashion. Previous claims that this theory is classically inconsistent are shown to be flawed, and the Velo-Zwanziger instability is proved to be absent. The theory propagates a massive spin-3/2 particle together with a spin-1/2 state whose mass is twice that of the j=3/2 mode. The causal construction of the quantum field is consistent with the field equations in that the ratio of the masses is the same, while it shows that the lower-spin component is a negative-norm state. The conformal anomaly is derived using known results for the heat kernel of nonminimal second-order operators, and the resulting $a$ charge is negative consistently with the Hofman-Maldacena bound, which applies only to unitary theories.