SYK-like tensor models on the lattice

We study large N tensor models on the lattice without disorder. We introduce techniques which can be applied to a wide class of models, and illustrate it by studying some specific rank-3 tensor models. In particular, we study Klebanov-Tarnopolsky model on lattice, Gurau-Witten model (by treating it as a tensor model on four sites) and also a new model which interpolates between these two models. In each model, we evaluate various four point functions at large N and strong coupling, and discuss their spectrum and long time behaviors. We find similarities as well as differences from SYK model. We also generalize our analysis to rank-D tensor models where we obtain analogous results as D = 3 case for the four point functions which we computed. For D > 5, we are able to compute the next-to-subleading 1/N corrections for a specific four point function.