Hints of unitarity at large $N$ in the $O(N)^3$ tensor field theory

We compute the OPE coefficients of the bosonic tensor model of cite{Benedetti:2019eyl} for three point functions with two fields and a bilinear with zero and non-zero spin. We find that all the OPE coefficients are real in the case of an imaginary tetrahedral coupling constant, while one of them is not real in the case of a real coupling. We also discuss the operator spectrum of the free theory based on the character decomposition of the partition function.