Half-wormholes in a complex SYK model

We compute the half-wormhole contribution in a complex SYK model with one time point by exact computations and saddle point analysis. The chemical potential significantly influences the computation and the relative magnitude of the half-wormhole. When the chemical potential is large compared to the random coupling, the disk dominates so that there's no wormhole and half-wormhole. When the chemical potential is relatively small we find out the wormhole and the half-wormhole contributions.