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

Abstract

We consider a model of Parisi where a single particle hops on an infinite-dimensional hypercube, under the influence of a uniform but disordered magnetic flux. We reinterpret the hypercube as the Fock-space graph of a many-body Hamiltonian and the flux as a frustration of the return amplitudes in Fock space. We will identify the set of observables that have the same correlation functions as the double-scaled Sachdev-Ye-Kitaev (DS-SYK) model, and hence the hypercube model is an equally good 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 similar frustrations. Hence we propose this type of Fock-space frustration as the broader characterization for NAdS${}_2$/NCFT${}_1$ microscopics, which encompasses the hypercube and the DS-SYK models as two specific examples. We then speculate on the possible origin of such frustrations.

published version

References in corpus (6)

• The bulk Hilbert space of double scaled SYK
• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Krylov complexity in large-$q$ and double-scaled SYK model
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Chaos on the hypercube
• Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS${}_2$/near-CFT${}_1$ duality

Cited by in corpus (5)

• The dilaton gravity hologram of double-scaled SYK
• Quantum group origins of edge states in double-scaled SYK
• Parisi's hypercube, Fock-space fluxes, and the microscopics of near-AdS${}_2$/near-CFT${}_1$ duality
• Unveiling Novel Insights in Quantum Dynamics through Extended Sachdev-Ye-Kitaev Model
• Bosonic near-CFT${}_1$ models from Fock-space fluxes