Phases of Euclidean wormholes in JT gravity

We present a JT gravity set up that reveals the evidence of (Euclidean) wormhole to black hole phase transition at finite charge density and/or chemical potential. identify low temperature system as charged solution. As is increased, it undergoes first order two density. At critical point (T=T0) transition, both Free energy (density) and discontinuous change. Finally, we conjectured field theory dual this gravitational two-site (uncoupled) complex SYK model