We revisit the work by Volkov and Soroka on spontaneously broken local
supersymmetry. It is demonstrated for the first time that, for specially chosen
parameters of the theory, the Volkov-Soroka action is invariant under two
different local supersymmetries. One of them is present for arbitrary values of
the parameters and acts on the Goldstino, while the other supersymmetry emerges
only in a special case and leaves the Goldstino invariant. The former can be
used to gauge away the Goldstino, and then the resulting action coincides with
that proposed by Deser and Zumino for consistent supergravity in first order
formalism. In this sense, pure $\mathcal{N} = 1$ supergravity is a special case
of the Volkov-Soroka theory. We also explain how the Volkov-Soroka approach
allows one to naturally arrive at the 1.5 formalism. Our analysis provides a
nonlinear realisation approach to construct unbroken $\mathcal{N} = 1$
Poincar\’e supergravity.

Source link


Leave A Reply