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

Abstract: 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 I. Klebanov and G. Tarnopolsky in JHEP 10 (2017) 037 [arXiv:1706.00839], which they checked numerically up to 8th order in the coupling constant.