Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?

TL;DR

This paper explores three-dimensional non-linear models of Goldstone fields related to higher-spin supersymmetry breaking, revealing that vector models relate to Chern-Simons actions and vector-spinor models generalize Rarita-Schwinger actions with hidden supersymmetry.

Contribution

It introduces new non-linear models of Goldstone fields for higher-spin supersymmetry breaking, connecting Chern-Simons and Rarita-Schwinger actions with hidden symmetries.

Findings

Vector Goldstone model's leading term is the Abelian Chern-Simons action.

Vector-spinor Goldstone model generalizes Rarita-Schwinger action while preserving gauge symmetry.

Hidden rigid supersymmetry acts non-linearly on the Rarita-Schwinger goldstino.

Abstract

We study three-dimensional non-linear models of vector and vector-spinor Goldstone fields associated with the spontaneous breaking of certain higher-spin counterparts of supersymmetry whose Lagrangians are of a Volkov-Akulov type. Goldstone fields in these models transform non-linearly under the spontaneously broken rigid symmetries. We find that the leading term in the action of the vector Goldstone model is the Abelian Chern-Simons action whose gauge symmetry is broken by a quartic term. As a result, the model has a propagating degree of freedom which, in a decoupling limit, is a quartic Galileon scalar field. The vector-spinor goldstino model turns out to be a non-linear generalization of the three-dimensional Rarita-Schwinger action. In contrast to the vector Goldstone case, this non-linear model retains the gauge symmetry of the Rarita-Schwinger action and eventually reduces to the latter by a non-linear field redefinition. We thus find that the free Rarita-Schwinger action is invariant under a hidden rigid supersymmetry generated by fermionic vector-spinor operators and acting non-linearly on the Rarita-Schwinger goldstino.