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arXiv · 1810.02146

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

Éric Fusy·Luca Lionni·Adrian Tanasa
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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.

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Éric Fusy, Luca Lionni, Adrian Tanasa. 2018-10-04. Combinatorial study of graphs arising from the Sachdev-Ye-Kitaev model. https://doi.org/10.1016/j.ejc.2019.103066

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