Correlation functions of $U(N)$-tensor models and their Schwinger–Dyson equations

Abstract

We analyze the correlation functions of $U(N)$-tensor models (or complex tensor models) and use the Ward–Takahashi identity in order to derive the full tower of exact, analytic Schwinger–Dyson equations. We write them explicitly for ranks $D=3$ and $D=4$. Throughout, we follow a non-perturbative approach. We propose the extension of this program to the Gurău–Witten model, a holographic tensor model based on the Sachdev–Ye–Kitaev model (SYK model).