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Parity violating vertices for spin-3 gauge fields

Nicolas Boulanger·Sandrine Cnockaert·Serge Leclercq
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Abstract

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincaré invariance and parity non-invariance, we classify all the nontrivial perturbative deformations of the abelian gauge algebra. In space-time dimensions $n=3$ and $n=5$, deformations of the free theory are obtained which make the gauge algebra non-abelian and give rise to nontrivial cubic vertices in the Lagrangian, at first order in the deformation parameter $g$. At second order in $g$, consistency conditions are obtained which the five-dimensional vertex obeys, but which rule out the $n=3$ candidate. Moreover, in the five-dimensional first order deformation case, the gauge transformations are modified by a new term which involves the second de Wit--Freedman connection in a simple and suggestive way.

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Nicolas Boulanger, Sandrine Cnockaert, Serge Leclercq. 2006-03-23. Parity violating vertices for spin-3 gauge fields. https://doi.org/10.1103/physrevd.73.065019

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