The $1/N$ expansion of the symmetric traceless and the antisymmetric tensor models in rank three

We prove rigorously that the symmetric traceless and the antisymmetric tensor models in rank three with tetrahedral interaction admit a 1 / N expansion, and that at leading order they are dominated by melon diagrams. This proves the recent conjecture of Klebanov and Tarnopolsky (JHEP 10:037, 2017. arXiv:1706.00839), which they checked numerically up to 8th order in the coupling constant.