Diagrammatics of the quartic O(N)3-invariant Sachdev-Ye-Kitaev-like tensor model

DOI10.1063/1.5095248zbMATH Open1416.81101arXiv1903.01723OpenAlexW2963050230MaRDI QIDQ5228066

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Publication date: 8 August 2019

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Abstract: Various tensor models have been recently shown to have the same properties as the celebrated Sachdev-Ye-Kitaev (SYK) model. In this paper we study in detail the diagrammatics of two such SYK-like tensor models: the multi-orientable (MO) model which has an $U(N)imesO(N)imesU(N)$ symmetry and a quartic $O(N{)}^3$-invariant model whose interaction has the tetrahedral pattern. We show that the Feynman graphs of the MO model can be seen as the Feynman graphs of the $O(N{)}^3$-invariant model which have an orientable jacket. We then present a diagrammatic toolbox to analyze the $O(N{)}^3$-invariant graphs. This toolbox allows for a simple strategy to identify all the graphs of a given order in the $1/N$ expansion. We apply it to the next-to-next-to-leading and next-to-next-to-next-to-leading orders which are the graphs of degree $1$ and $3/2$ respectively.

Full work available at URL: https://arxiv.org/abs/1903.01723

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