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arXiv · 1706.07358

Correlation functions of $\mathrm{U}(N)$-tensor models and their Schwinger-Dyson equations

Romain Pascalie·Carlos I. Pérez-Sánchez·Raimar Wulkenhaar
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Abstract

We analyse the correlation functions of $\mathrm{U}(N)$-tensor models (or complex tensor models), which turn out to be classified by boundary graphs, and use the Ward-Takahashi identity and the graph calculus developed in [Commun. Math. Phys. (2018) 358: 589] in order to derive the complete tower of exact, analytic Schwinger-Dyson equations for correlation functions with connected boundary graphs. We write them explicitly for ranks $D=3$ and $D=4$. Throughout, we follow a non-perturbative approach to Tensor (Group) Field Theories. We propose the extension of this program to the Gurau-Witten model, a holographic tensor model based on the Sachdev-Ye-Kitaev model (SYK model).

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Romain Pascalie, Carlos I. Pérez-Sánchez, Raimar Wulkenhaar. 2017-06-22. Correlation functions of $\mathrm{U}(N)$-tensor models and their Schwinger-Dyson equations. https://doi.org/10.4171/aihpd/107

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