  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.

High Energy Physics - Theory;Strongly Correlated Electrons;Quantum Physics