Master actions and helicity decomposition for spin-4 models in 3D

The present work introduces a master action which interpolates between four self-dual models, SD(i), describing massive spin-4 particles in D=2+1 dimensions. These models are designated by i=1,2,3 and 4, representing the order in derivatives. Our results show that the four descriptions are quantum equivalents by comparing their correlation functions, up to contact terms. This is an original result since that a proof of quantum equivalence among these models have not been demonstrated in the literature. Besides, a geometrical approach is demonstrated to be a useful tool in order to describe the third and fourth order in derivatives models. On the other hand, the construction of the master action relies on the introduction of mixing terms, which must be free of particle content. Here, we demonstrate how the helicity decomposition method can be used in order to verify the absence of particle content of such terms, ensuring the proper usability of the master action technique. This kind of result can be very useful in situations where we do not have access to the higher spin-projection basis which would allow the analysis to be handle by explicitly calculating the propagator and subsequently analysing its poles.