Parity violating vertices for spin-3 gauge fields

TL;DR

This paper classifies all possible consistent parity-violating interactions for spin-3 gauge fields in Minkowski space, identifying specific deformations in 3 and 5 dimensions that alter the gauge algebra and introduce nontrivial cubic vertices.

Contribution

It provides a complete classification of parity-violating deformations of spin-3 gauge theories, highlighting unique features in five dimensions and ruling out certain deformations in three dimensions.

Findings

Deformations in 3 and 5 dimensions make the gauge algebra non-abelian.

First order deformations introduce nontrivial cubic vertices.

Second order consistency conditions restrict possible deformations in 5 dimensions.

Abstract

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincar\'e 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.