Local supersymmetry: Variations on a theme by Volkov and Soroka
Abstract
As is well known, supergravity was discovered in 1976 by Ferrara, Freedman and van Nieuwenhuizen, and independently by Deser and Zumino. In 1994, Volkov, one of the cocreators of supersymmetry, posted two preprints to the hepth archive containing "supergravity before 1976" in the title. He argued that the key ingredients of $\mathcal{N} = 1$ supergravity in four dimensions had appeared in his earlier work with Soroka on the superHiggs effect. In order to better appreciate his point of view, in this paper we first revisit the VolkovSoroka construction and review it. Then we demonstrate that, for specially chosen parameters of the theory, the VolkovSoroka 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 this sense, pure $\mathcal{N} = 1$ supergravity is a special case of the VolkovSoroka theory, and it could have been discovered before 1976.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.12835
 Bibcode:
 2021arXiv211012835K
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 13 pages