The local SYK model and its triple-scaling limit

We study a model of fermions with random couplings similar to conventional SYK with N number of flavours of fermions, at large N. Unlike the conventional SYK model, which has all-to-all couplings, the model we study, which we call local SYK, has a much less number of random couplings, just N in number and with only local interactions. It is shown that there exists a limit in which the local SYK model can be solved using the chord diagram techniques, analogous to the double-scaled limit of conventional SYK. This limit corresponds to taking the size of the fermion coupling terms, q, to scale linearly with N. A further triple-scaling limit is taken to analyze the low energy limit and it is shown that the OTOCs saturate the chaos bound, paralleling the analysis in the conventional SYK.