Internal Supersymmetry and Small-field Goldstini

TL;DR

This paper explores a novel small-field limit of Goldstino dynamics in supersymmetry, revealing an internal supersymmetry algebra and connections to Galilean scalar theories, with implications for higher-dimensional models.

Contribution

It introduces a new small-field Goldstino model with an internal supersymmetry algebra, linking it to Galilean scalar theories and extending to higher dimensions.

Findings

The small-field Goldstino exhibits an internal supersymmetry algebra.

It is analogous to Galilean scalar theories like the Dirac-Born-Infeld limit.

The model generalizes to extended internal supersymmetry and higher dimensions.

Abstract

The dynamics of the Goldstino mode of spontaneously broken supersymmetry is universal, being fully determined by the non-linearly realized symmetry. We investigate the small-field limit of this theory. This model non-linearly realizes an alternative supersymmetry algebra with vanishing anti-commutators between the fermionic generators, much like an internal supersymmetry. This Goldstino theory is akin to the Galilean scalar field theory that arises as the small-field limit of Dirac-Born-Infeld theory and non-linearly realizes the Galilean symmetry. Indeed, the small-field Goldstino is the partner of a complex Galilean scalar field under conventional supersymmetry. We close with the generalization to extended internal supersymmetry and a discussion of its higher-dimensional origin.