The full Schwinger-Dyson tower for random tensor models

TL;DR

This paper develops a comprehensive non-perturbative framework for complex tensor field theories, deriving an exact tower of Schwinger-Dyson equations for all correlation functions with boundary graphs, advancing the understanding of random tensor models.

Contribution

It introduces a full Schwinger-Dyson tower for tensor models with quartic interactions, providing a systematic non-perturbative approach and classifying correlation functions by boundary graphs.

Findings

Derived the Ward-Takahashi identity for tensor field theories.

Established the exact Schwinger-Dyson equations for all correlation functions.

Classified correlation functions using boundary graphs.

Abstract

We treat random rank-$D$ tensor models as $D$-dimensional quantum field theories---tensor field theories (TFT)---and review some of their non-perturbative methods. We classify the correlation functions of complex tensor field theories by boundary graphs, sketch the derivation of the Ward-Takahashi identity and stress its relevance in the derivation of the tower of exact, analytic Schwinger-Dyson equations for all the correlation functions (with connected boundary) of TFTs with quartic pillow-like interactions.