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

Understand

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.