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

TL;DR

This paper rigorously establishes a $1/N$ expansion for rank-three symmetric traceless and antisymmetric tensor models with tetrahedral interactions, confirming the dominance of melon diagrams at leading order as conjectured by Klebanov and Tarnopolsky.

Contribution

It provides a rigorous proof of the $1/N$ expansion and leading-order behavior in these tensor models, confirming previous numerical conjectures.

Findings

Proved the existence of a $1/N$ expansion for the models.

Established that melon diagrams dominate at leading order.

Confirmed the conjecture by Klebanov and Tarnopolsky through rigorous analysis.

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.