Diagrammatics of the quartic $O(N)^3$-invariant Sachdev-Ye-Kitaev-like tensor model
Résumé
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 multiorientable (MO) model which has a U(N) × O(N) × U(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. Then, we 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.