Parisi's Hypercube, Fock-Space Frustration, and Near-AdS_{2}/Near-CFT_{1} Holography.

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.

Onset of Quantum Chaos in Random Field Theories.

We study the quantum Lyapunov exponent λ_{L} in theories with spacetime-independent disorder. We first derive self-consistency equations for the two- and four-point functions for products of N models coupled by disorder at large N, generalizing the equations appearing in SYK-like models. We then study families of theories in which the disorder coupling is an exactly marginal deformation, allowing us to follow λ_{L} from weak to strong coupling. We find interesting behaviors, including a discontinuous transition into chaos, mimicking classical KAM theory.