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We study a model of fermions with random couplings similar to conventionalSYK with $N$ number of flavours of fermions, at large $N$. Unlike theconventional 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 alimit in which the local SYK model can be solved using the chord diagramtechniques, analogous to the double-scaled limit of conventional SYK. Thislimit corresponds to taking the size of the fermion coupling terms, $q$, toscale linearly with $N$. A further triple scaling limit is taken to analyze thelow energy limit and it is shown that the OTOCs saturate the chaos bound,paralleling the analysis in the conventional SYK.

The local SYK model and its triple scaling limit