Connect infrared memory, finite-size dynamics, and holographic behavior in the coupled-SYK junction

Establish the precise large-$N$, finite-$N$, and holographic connections among infrared sensitivity, quantum-information transfer, and many-body scrambling in the dynamically opened coupled-SYK Majorana junction.

Background

The paper studies a time-dependent bilinear coupling that dynamically opens a junction between two interacting $q=4$ Sachdev–Ye–Kitaev systems. Its large-$N$ conformal analysis predicts an effective anomalous response with Hilbert–Schmidt norm scaling as $1/\mu$ in the infrared, while exact finite-$N$ calculations show parity transfer, entanglement generation, and cross-sector operator spreading. These analytical and numerical results describe complementary regimes, but the paper does not establish how the continuum large-$N$ infrared behavior emerges from finite-size dynamics.

The paper also proposes a nearly-$AdS_2$ interpretation in which the time-dependent coupling acts as a dynamical boundary source. A complete connection among the fermionic infrared memory, regulated finite-$N$ observables, and the response or backreaction of the nearly-$AdS_2$ soft modes remains unresolved. Establishing this relationship would unify the paper’s three main themes: infrared sensitivity, quantum-information transfer, and many-body scrambling.