Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS2/near-CFT1 duality

Parisi's hypercube model describes a charged particle hopping on a d-dimensional hypercube with disordered background fluxes in the large d limit. It was noted previously [Jia and Verbaarschot, J. High Energy Phys. 11 (2020) 154JHEPFG1029-847910.1007/JHEP11(2020)154] that the hypercube model at leading order in 1/d has the same spectral density as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model. In this work we identify the set of observables that have the same correlation functions as the DS-SYK model, demonstrating that the hypercube model is an equally good microscopic model for near-AdS2/near-CFT1 holography. Unlike the SYK model, the hypercube model is not p-local. Rather, we note that the shared feature between the two models is that they both have a large amount of disordered but uniform fluxes on their Fock-space graphs, and we propose this is a broader characterization of near-CFT1 microscopics. Moreover, we suggest that the hypercube model can be viewed as the operator growth model of the DS-SYK model. We explain some universality in subleading corrections and relate them to bulk vertices. Finally, we revise a claim made in the aforementioned reference about the existence of a spectral gap.