Abstract
A
bstract
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-
$$ \frac{3}{2} $$
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-
$$ \frac{3}{2} $$
3
2
mixing has no local Dirac-gaugino-type
$$ \mathcal{N} $$
N
= 1 superspace realization: a superspace description requires projection onto the transverse superspin-
$$ \frac{3}{2} $$
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.