Minimal Off-Shell Version of N = 1 Chiral Supergravity

TL;DR

This paper develops a minimal off-shell formulation of N=1 chiral supergravity by introducing auxiliary fields, ensuring the supersymmetry algebra closes off-shell and includes additional gauge transformations.

Contribution

It presents the first minimal off-shell formulation of N=1 chiral supergravity with auxiliary fields that close the SUSY algebra off-shell and incorporate extra gauge symmetries.

Findings

Supersymmetry algebra closes off-shell with auxiliary fields.

Auxiliary fields include a complex antisymmetric tensor and an axial-vector.

Additional gauge transformations are generated in the off-shell formulation.

Abstract

We construct the minimal off-shell formulation of N = 1 chiral supergravity (SUGRA) introducing a complex antisymmetric tensor field $B_{\mu \nu}$ and a complex axial-vector field $A_{\mu}$ as auxiliary fields. The resulting algebra of the right- and left-handed supersymmetry (SUSY) transformations closes off shell and generates chiral gauge transforamtions and vector gauge transformations in addition to the transformations which appear in the case without auxiliary fields.