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We consider a model of Parisi where a single particle hops on aninfinite-dimensional hypercube, under the influence of a uniform but disorderedmagnetic flux. We reinterpret the hypercube as the Fock-space graph of amany-body Hamiltonian, and the flux as a frustration of the return amplitudesin Fock space. We will show that this model has the same correlation functionsas the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model, and hence is an equallygood quantum model for near-AdS$_2$/near-CFT$_{1}$ (NAdS$_2$/NCFT$_1$)holography. Unlike the SYK model, the hypercube Hamiltonian is not $p$-local.Instead, the SYK model can be understood as a Fock-space model with similarfrustrations. Hence we propose this type of Fock-space frustration as thebroader characterization for NAdS$_2$/NCFT$_1$ microscopics, and speculate thepossible origin of such frustrations.

Parisi's hypercube, Fock-space frustration and near-AdS$_2$/near-CFT$_1$ holography