Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS${}_2$/near-CFT${}_1$ duality

Abstract

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) 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-AdS${}_2$/near-CFT${}_1$ 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-CFT${}_1$ 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 the aforementioned reference about the existence of a spectral gap.

arXiv commentThe companion paper of arxiv.org/abs/2303.18182

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Cited by in corpus (4)

• Tridiagonal Hamiltonians modeling the density of states of the Double-Scaled SYK model
• Parisi's hypercube, Fock-space frustration and near-AdS${}_2$/near-CFT${}_1$ holography
• Unveiling Novel Insights in Quantum Dynamics through Extended Sachdev-Ye-Kitaev Model
• Bosonic near-CFT${}_1$ models from Fock-space fluxes