On the role of torsion and higher forms in off-shell supergravity

The presence of a nonvanishing totally antisymmetric (super)torsion, equivalent to an axial vector, and higher forms in the "new minimal" and "old minimal" off-shell formulations of $N$ = 1, D = 4 supergravity is elaborated. The geometric superspace approach and study both the geometric Lagrangian and the off-shell closure of the Bianchi identities in this framework, showing how the aforementioned axial vector torsion contributes to both the new and the old minimal set of auxiliary fields is adopted. In particular, to reproduce (a variant of) the old minimal set within the geometric setup, two real auxiliary 3-form potentials. (© 2023 The Authors. Fortschritte der Physik published by Wiley‐VCH GmbH)