(Pseudo-)Dirac Gravitinos

TL;DR

This paper explores the theoretical implications of a Dirac gravitino in low-energy supersymmetry, analyzing its properties, matter couplings, and potential phenomenological consequences within specific supersymmetry breaking frameworks.

Contribution

It provides a detailed analysis of Dirac gravitino properties, their realization in supergravity, and implications for matter couplings and neutrino mass generation.

Findings

Degenerate Majorana modes form a Dirac gravitino in Scherk--Schwarz breaking.

Standard gravitino couplings lead to negative scalar thresholds in minimal models.

Dirac fermion masses depend on additional matter currents and UV completion details.

Abstract

We discuss low-energy effective theories with a Dirac gravitino. Our main benchmark is Scherk--Schwarz supersymmetry breaking with anti-periodic boundary conditions for fermions on S^1/Z_2. In this case two Majorana spin-3/2 modes are degenerate, so the low-energy theory is naturally organized around a Dirac gravitino and an associated R-symmetry selection rule. We show, in minimal supergravity, that this Dirac spin-3/2 mixing has no local Dirac-gaugino-type N=1 superspace realization: a superspace description requires projection onto the transverse superspin-3/2 sector. We then analyze some consequences for matter couplings and radiative masses. The ordinary gravitino supercurrent coupling gives the standard universal Scherk--Schwarz scalar threshold; in the minimal benchmark this contribution is negative, and should therefore be regarded as one calculable contribution to the scalar mass matrix, not as a complete scalar-spectrum prediction. Dirac fermion masses can be generated if an additional companion-channel matter current is present. The existence and normalization of this current are not fixed by the Dirac gravitino alone and depend on the ultraviolet completion. We finally discuss small R-breaking deformations, the resulting pseudo-Dirac regime, and comment on possible applications to singlet fermions, modulini, and radiative Dirac neutrino masses.