Annales de l’Institut Henri Poincaré D


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Published online first: 2021-09-17
DOI: 10.4171/AIHPD/107

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

Romain Pascalie[1], Carlos I. Pérez-Sánchez[2] and Raimar Wulkenhaar[3]

(1) Westfälische Wilhelms-Universität Münster, Germany
(2) Westfälische Wilhelms-Universität Münster, Germany
(3) Westfälische Wilhelms-Universität Münster, Germany

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).

Keywords: Quantum field theory, tensor models, tensor field theory, Schwinger–Dyson equations, quantum gravity, combinatorics

Pascalie Romain, Pérez-Sánchez Carlos I., Wulkenhaar Raimar: Correlation functions of U($N$)-tensor models and their Schwinger–Dyson equations. Ann. Inst. Henri Poincaré Comb. Phys. Interact. Electronically published on September 17, 2021. doi: 10.4171/AIHPD/107 (to appear in print)