M. Tsuda et T. Shirafuji, MINIMAL OFF-SHELL VERSION OF N=1 CHIRAL SUPERGRAVITY - ART. NO. 087702, Physical review. D. Particles and fields, 5808(8), 1998, pp. 7702
We construct the minimal off-shell formulation of N=1 chiral supergrav
ity introducing a complex antisymmetric tensor field B-mu nu and a com
plex axial-vector field A(mu) as auxiliary fields. The resulting algeb
ra of the right- and left-handed supersymmetry transformations closes
off shell and generates chiral gauge transformations and vector gauge
transformations in addition to the transformations which appear in the
case without auxiliary fields. [S0556-2821(98)06718-6].