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

TL;DR

This paper investigates the unitarity properties of the large N limit in a bosonic tensor field theory by analyzing OPE coefficients and operator spectra, revealing conditions under which these coefficients are real or complex.

Contribution

It provides the first detailed computation of OPE coefficients in the bosonic tensor model, highlighting the impact of coupling constant choices on unitarity.

Findings

OPE coefficients are real with imaginary coupling constant.

One OPE coefficient becomes non-real with real coupling.

Operator spectrum analyzed via character decomposition.

Abstract

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.