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 super-symmetry generated by fermionic vector-spinor operators and acting non-linearly on the Rarita-Schwinger goldstino.
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Bansal, S., Sorokin, D. Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?. J. High Energ. Phys. 2018, 106 (2018). https://doi.org/10.1007/JHEP07(2018)106
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DOI: https://doi.org/10.1007/JHEP07(2018)106