The Two Lives of a Massive Charged Spin-$\tfrac32$ Particle: from Superstrings EFT to Supergravity

TL;DR

This paper explores two different realizations of a charged massive spin-3/2 particle, analyzing their properties, differences, and how they relate to supergravity and string theory, with implications for understanding their interactions with gravity and electromagnetic fields.

Contribution

It constructs a continuous interpolation between supergravity and flat-space Fierz--Pauli systems for spin-3/2 particles, revealing how gravity influences their structure and gyromagnetic properties.

Findings

Both systems achieve gyromagnetic ratio g=2 via non-minimal couplings.

The chiral asymmetry in the flat-space system is resolved when gravity is dynamical.

The supergravity endpoint is uniquely compatible with dynamical gravity and non-constant electromagnetic fields.

Abstract

A charged massive spin-$\tfrac32$ field in a constant electromagnetic background admits two familiar realizations. In supergravity, where it is identified with a gravitino, its mass and charge are tied in Planck units. In the decoupled-gravity regime, the two-derivative Fierz--Pauli system describing the first massive open-string modes instead allows arbitrary mass and charge. The gyromagnetic ratio $g=2$ is achieved in both cases through non-minimal Pauli couplings, but these take different forms: they are symmetric in the two chiral sectors in the supergravity system, and chiral-asymmetric in the flat-space one. We construct a continuous family of Fierz--Pauli systems interpolating between these two endpoints. We show that the corresponding second-order equations always reproduce $g=2$ at linear order, but generically contain a chiral $F^2$ term at quadratic order. Its coefficient vanishes precisely at the two endpoint theories. Requiring compatibility with dynamical gravity, or closure for non-constant electromagnetic field strength, then selects the supergravity endpoint. The result clarifies the domains of applicability of the two systems and shows that the maximally asymmetric organization of the decoupled theory cannot be extended unchanged once gravity is dynamical. For comparison, we also analyze a charged massive spin-$2$ field on Einstein--Maxwell backgrounds and exhibit the corresponding closure of the associated lower-spin chain.