A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics

We study a bipartite version of the Sachdev-Ye-Kitaev (SYK) model. We show that the model remains solvable in the limit of large-$N$ in the same sense as the original model if the ratio of both flavors is kept finite. The scaling dimensions of the two species can be tuned continuously as a function of the ratio. We also investigate the finite-size spectral properties of the model. We show how the level statistics differs from the original SYK model and infer an additional exchange symmetry in the bipartite model.