Resolving the Replica Problem with Supersymmetric SYK Models

We investigate the SYK model with arbitrary replicas and solvable replica wormholes. First, we consider copies of non-supersymmetric SYK models with additional random interactions. We find this method is solvable under special conditions. Then we introduce the $N=1$ supersymmetric SYK model and use the fractal symmetry to cover the replica structure.  We study the dynamics in Lorentzian time and plotted the effective action evolving over time. Furthermore, we focus on the emergent superconformal symmetry in the low-energy limit with replicas. We consider corresponding constraints on N=1 super-JT gravity for holographic matching.  We also verify the modular entropy, n-dependence of the relative entropy, and capacity of entanglement using fully diagonal methods.