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