On the Goldstino actions and their symmetries

TL;DR

This paper analyzes the symmetries of Goldstino actions starting from the Akulov-Volkov action, identifying a group of transformations that preserve their structure, and establishing explicit relations among five different Goldstino models.

Contribution

It constructs a finite-dimensional Lie group of transformations preserving Goldstino actions and derives explicit maps and symmetries among five known Goldstino models.

Findings

Identified a 12-parameter subgroup of trivial symmetries.

Derived explicit field redefinitions connecting five Goldstino actions.

Determined off-shell nonlinear supersymmetry transformations for these actions.

Abstract

Starting from the Akulov-Volkov (AV) action, we compute a finite-dimensional Lie group G of all field transformations of the form \lambda -> \lambda ' = \lambda + O(\lambda ^3) which preserve the functional structure of low-energy Goldstino-like actions. Associated with G is its twelve-parameter subgroup H of trivial symmetries of the AV action. The coset space G/H is naturally identified with the space of all Goldstino models. We then apply our construction to study the properties of five different Goldstino actions available in the literature. Making use of the most general field redefinition derived, we find explicit maps between all five cases. In each case there is a twelve- parameter freedom in these maps due to trivial symmetries inherent in the Goldstino actions. Finally, by using the pushforward of the AV supersymmetry, we find the off-shell nonlinear supersymmetry transformations of the other five actions and compare to those normally associated with these actions.