Local supersymmetry: Variations on a theme by Volkov and Soroka

TL;DR

This paper explores the invariance properties of the Volkov-Soroka action under different local supersymmetries, revealing connections to supergravity and the 1.5 formalism through a nonlinear realization approach.

Contribution

It demonstrates that the Volkov-Soroka action exhibits two distinct local supersymmetries under specific parameters, linking it to pure supergravity and the 1.5 formalism.

Findings

Two different local supersymmetries identified in Volkov-Soroka action.

Pure $ abla$ supergravity is a special case of the Volkov-Soroka theory.

The approach offers a nonlinear realization method for unbroken $ abla$ supergravity.

Abstract

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 the first-order formalism. In this sense, pure $\mathcal{N} = 1$ supergravity is a special case of the Volkov-Soroka theory, although it was not discovered by these authors. 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.