Abstract
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.
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Acknowledgments
We thank Micha Berkooz, Prithvi Narayan, Onkar Parrikar, Harshit Rajgadia, Sandip Trivedi and MasatakaWatanabe for helpful discussions. We also thank Arkaprava Mukherjee and Sandip Trivedi for collaboration on [8]. The work of TA and NI were supported in part by JSPS KAKENHI Grant Number 21J20906(TA), 18K03619(NI). The work of NI and SS were also supported by MEXT KAKENHI Grant-in-Aid for Transformative Research Areas A “Extreme Universe” No. 21H05184.
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Anegawa, T., Iizuka, N. & Sake, S.K. The local SYK model and its triple-scaling limit. J. High Energ. Phys. 2023, 160 (2023). https://doi.org/10.1007/JHEP10(2023)160
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DOI: https://doi.org/10.1007/JHEP10(2023)160