Combinatorial study of graphs arising from the Sachdev-Ye-Kitaev model

Abstract

We consider the graphs involved in the theoretical physics model known as the colored Sachdev-Ye-Kitaev (SYK) model. We study in detail their combinatorial properties at any order in the so-called $1/N$ expansion, and we enumerate these graphs asymptotically. Because of the duality between colored graphs involving $q+1$ colors and colored triangulations in dimension $q$, our results apply to the asymptotic enumeration of spaces that generalize unicellular maps - in the sense that they are obtained from a single building block - for which a higher-dimensional generalization of the genus is kept fixed.

arXiv comment22 pages, 13 figures

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• Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
• Diagrammatics of the quartic $O(N{)}^3$-invariant Sachdev-Ye-Kitaev-like tensor model
• Classifying compact 4-manifolds via generalized regular genus and G-degree
• New Limits for Large $N$ Matrix and Tensor Models: Large $D$, Melons and Applications